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# Index to 2D 5-Neighbor Cellular Automata

Index to 2D 5-Neighbor Outer Totalistic Cellular Automata

Sequences in the OEIS related to 2D 5-Neighbor Outer Totalistic Cellular Automata are tabulated here.

## Introduction

There are 2^32 possible rules for general two-dimensional Cellular Automata. Totalistic rules depend only upon the total number of ON cells in a neighborhood. Outer Totalistic rules also include the state of the center cell. The 5-Neighbor Outer Totalistic rules include the center cell and those to the N, E, S and W of it. 9-Neighbor rules would also consider neighbors that are diagonal to the center cell.

There are 1024 possible 2D 5-Neighbor Outer Totalistic Cellular Automata. Wolfram's numbering scheme identifies these by rule numbers from 0 to 1023. See "A New Kind of Science" by Stephen Wolfram, pages 170-179 or the Eric Weisstein's "World of Mathematics" links below. The sequences in the OEIS generally represent a two-dimensional cellular automata (CA) on a square grid representing successive generations or stages. This grid is initialized by a single black (ON) cell. Some rules will generate ON cells that nearly fill any grid size at stage 1. See rule 777 for example. So, in order to ensure finite values in these sequences, the grid is restricted to grow at only one cell in each direction at each stage. Thus, at stage n, the grid under consideration is 2n+1 cells on each side. Due to the definition of the rules and being initiated by a single cell, all resulting diagrams are symmetric along each axis and along each diagonal.

An example. The base 2 digits of the rule number determines the CA evolution. The last bit specifies the state of a cell if all neighbors are OFF and it too is OFF. The next to last bit specifies the state of a cell if all neighbors are OFF but the cell itself is ON. Then each earlier pair of bits specifies what should happen if progressively (Totalistic) more neighbors are black. So, bits 2^0 and 2^1 apply if none of the four neighbors are ON, bits 2^2 and 2^3 apply if one neighbor is ON, bits 2^4 and 2^5 apply if two neighbors are ON, bits 2^6 and 2^7 apply if three neighbors are ON and bits 2^8 and 2^9 apply if all four neighbors are ON. For example, Rule 614 equates to the bits {1,0,0,1,1,0,0,1,1,0}. Since we are considering 5-Neighbor Outer Totalistic CA the future state of a cell is determined by the four nearest neighbors (N,E,S,W) and the cell itself. Progressing from stage 0 to stage 1 we have to determine the new state of nine cells. The first cell (upper left corner) has the initial state of OFF and all neighbors are OFF, so bit 2^0 applies dictating that the new state is OFF. The second cell (middle of top row) has the initial state of OFF and one of its neighbors (the original ON cell from stage 0) is ON. One neighbor is ON so bits 2^2 and 2^3 apply. Since the initial state is OFF, bit 2^2 applies dictating that the new state is ON. Now skipping to the cell at the origin, no neighbors are ON and the initial state is ON, so bit 2^1 applies to dictate that the new state is ON. For rule 614, a more specific statement of the rule can be stated. The state of the cell is turned ON or remains ON only if an odd number of these five cells are ON. The first five stages (0-4) of the CA generated by Rule 614 are:

```       Stage 0             Stage 1             Stage 2            Stage 3            Stage 4
. . . . x . . . .
. . . x . . .    . . . . . . . . .
. . x . .        . . x x x . .    . . . . . . . . .
. x .             . . . . .        . x . . . x .    . . . . . . . . .
x                 x x x             x . x . x        x x . x . x x    x . . . x . . . x
. x .             . . . . .        . x . . . x .    . . . . . . . . .
. . x . .        . . x x x . .    . . . . . . . . .
. . . x . . .    . . . . . . . . .
. . . . x . . . .

```

Certain attributes of these CA can be interpreted as integer sequences. These are tabulated in the tables below. Perhaps the simplest attribute is the total number of ON cells at each stage. For example, the sequence generated by Rule 614 begins: 1,5,5,17,5,25,17,61,5,25,25,85 (A072272). Another sequence are the terms above only at at stages 2^n-1. This is relevant in the analysis of sequences such as Rule 614. See Sloane reference, "On the number of ON Cells in Cellular Automata" link below. The sequence generated by Rule 614 for this attribute begins: 1,5,17,61,217,773,2753 (A007483). Another sequence is the first difference of the total number of ON cells at each stage. This is simply the number of ON cells added at each stage, which could be negative. The sequence generated by Rule 614 for this attribute begins: 4,0,12,-12,20,-8,44,-56,20 (A170878). Another sequence is the partial sum of the total number of ON cells at each stage. This represents the total number of ON cells through n stages. The sequence generated by Rule 614 for this attribute begins: 1,6,11,28,33,58,75,136,141 (A253908).

Certain CA definitions (or rules), while different, generate identical sequences based solely on the number of ON cells. For example, rules 675 and 899 have different diagram sequences but have identical number of ON cells at each stage. The table below consolidates these rules that generate identical number of ON cells at each stage for the first 50 terms. It is conjectured that the ON cells remain identical for all terms for these rules.

Often a well known sequence like A005408 (The Odd Integers) comes very close to the CA generated sequence. The first term, usually a zero, may be missing or substituted. Or an extra first term will be present. In these cases the well known sequence is used in the tables below and the sequence is indicated with an asterisk. For example, the partial sums sequence based on Rule 4 begins 1,5,9,25,29,45,61,125. The OEIS sequence A116520 begins 0,1,5,9,25,29,45,61,125. This is a close match and will be used in the table below for Rule 4.

## Sequences in the OEIS Related to 2D 5-Neighbor Outer Totalistic Cellular Automata Describing the Total Number of ON Cells

```Column headings in the table below:

Rule         Wolfram's Rule Number(s)
Sequence     First seven terms of the number of ON cells sequence
ON           A-number of the sequence listing the number of ON cells at each stage of the CA evolution
ON(2^n-1)    A-number of the sequence listing the number of ON cells at stages 2^n-1, n=0,...
Partial Sum  A-number of the sequence listing the partial sums of the number of ON cells at each stage
First Diff   A-number of the sequence listing the first differences of the number of ON cells at each stage
(an asterisk, "*", in an A-number indicates a near match)
```

2D 5-Neighbor Outer Totalistic Cellular Automata Sequences in the OEIS
Rule Sequence ON ON(2^n-1) Partial Sum First Diff
0,8,16,24,32,40,48,56,64,72,80,88,96,104,112,120,128,136,144, 152,160,168,176,184,192,200,208,216,224,232,240,248,256,264, 272,280,288,296,304,312,320,328,336,344,352,360,368,376,384, 392,400,408,416,424,432,440,448,456,464,472,480,488,496,504, 512,520,528,536,544,552,560,568,576,584,592,600,608,616,624, 632,640,648,656,664,672,680,688,696,704,712,720,728,736,744, 752,760,768,776,784,792,800,808,816,824,832,840,848,856,864, 872,880,888,896,904,912,920,928,936,944,952,960,968,976,984, 992,1000,1008,1016 1,0,0,0,0,0,0 A000007 A000007 A000012 A154955*
1,9,17,25,257,265,273,281 1,4,1,44,1,116,1 A269906 A269907 A269908 A269909
2,10,18,26,34,42,50,58,66,74,82,90,98,106,114,122,130,138,146, 154,162,170,178,186,194,202,210,218,226,234,242,250,258,266, 274,282,290,298,306,314,322,330,338,346,354,362,370,378,386, 394,402,410,418,426,434,442,450,458,466,474,482,490,498,506, 514,522,530,538,546,554,562,570,578,586,594,602,610,618,626, 634,642,650,658,666,674,682,690,698,706,714,722,730,738,746, 754,762,770,778,786,794,802,810,818,826,834,842,850,858,866, 874,882,890,898,906,914,922,930,938,946,954,962,970,978,986, 994,1002,1010,1018 1,1,1,1,1,1,1 A000012 A000012 A000027 A000004
3,11,19,27,67,75,83,91 1,5,1,45,1,117,1 A269910 A269911 A269912 A269913
4,12,36,44,68,76,100,108,132,140,164,172,196,204,228,236,516, 524,548,556,580,588,612,620,644,652,676,684,708,716,740,748 1,4,4,16,4,16,16 A102376 A000302 A116520* A269880
5,13,21,29,37,45,53,61,69,77,85,93,101,109,117,125 1,8,0,49,0,121,0 A270006 A270007 A270008 A270009
6,38,70,102,134,166,198,230 1,5,4,20,4,20,16 A269695 A269696 A269697 A269698
7,15,23,31,39,47,55,63,71,79,87,95,103,111,119,127,135,143,151, 159,167,175,183,191,199,207,215,223,231,239,247,255,263,271, 279,287,295,303,311,319,327,335,343,351,359,367,375,383,391, 399,407,415,423,431,439,447,455,463,471,479,487,495,503,511 1,9,0,49,0,121,0 A270010 A270011 A270012 A270013
14,46,142,174 1,5,8,20,20,32,40 A269707 A269708 A269709 A269710
20,28,52,60,148,156,180,188,532,540,564,572,660,668,692,700 1,4,8,12,20,24,44 A269711 A269712 A269713 A269714
22 1,5,8,20,16,44,32 A269715 A269716 A269717 A269718
30 1,5,12,16,36,24,60 A269753 A269754 A269755 A269756
33 1,4,5,32,9,92,21 A269810 A269811 A269812 A269813
35 1,5,5,37,9,101,21 A269814 A269815 A269816 A269817
41 1,4,5,32,13,84,29 A269872 A269873 A269874 A269875
43,59 1,5,5,37,13,97,25 A269876 A269815 A269878 A269879
49 1,4,5,32,9,100,21 A270014 A270015 A270016 A270017
51 1,5,5,37,9,109,13 A270018 A270019 A270020 A270021
54 1,5,8,20,28,40,44 A270022 A270023 A270024 A270025
57 1,4,5,32,13,84,29 A270075 A270076 A270077 A270078
62 1,5,12,20,32,44,68 A270079 A270080 A270081 A270082
65,321 1,4,5,36,9,96,17 A269782 A270084 A270085 A270086
73 1,4,5,40,0,121,0 A270087 A270088 A270089 A270090
78 1,6,14,34,54,86,134 A270091 A270092 A270093 A270094
81 1,4,5,40,9,100,21 A270098 A270099 A270100 A270101
84,92,116,124,212,220,244,252,596,604,628,636,724,732,756,764 1,4,8,16,16,32,32 A189007 A000302 A270106 A270107
86 1,5,8,24,16,48,32 A270125 A270126 A270127 A270128
89 1,4,5,44,0,121,0 A270129 A270130 A270131 A270132
94 1,5,12,16,36,24,60 A270133 A270134 A270135 A270136
97 1,4,9,32,13,84,21 A270152 A270153 A270154 A270155
99 1,5,5,41,12,109,16 A270156 A270157 A270158 A270159
105 1,4,9,32,13,92,45 A270160 A270161 A270162 A270163
107 1,5,5,41,12,109,16 A270164 A270165 A270166 A270167
110 1,5,8,20,20,32,48 A270168 A270169 A270170 A270171
113 1,4,9,32,17,88,37 A270177 A270178 A270179 A270180
115 1,5,5,41,12,109,16 A270181 A270182 A270183 A270184
118 1,5,8,24,24,48,36 A270185 A270186 A270187 A270188
121 1,4,9,32,17,100,40 A270206 A270207 A270208 A270209
123 1,5,5,41,12,109,16 A270210 A270211 A270212 A270213
126 1,5,12,20,36,40,80 A270214 A173034 A270215 A270216
129,385 1,4,5,28,9,84,21 A270217 A270218 A270219 A270220
131 1,5,5,33,13,93,25 A270221 A270222 A270223 A270224
133 1,8,4,40,17,100,25 A270232 A270233 A270234 A270235
137 1,4,5,28,9,84,29 A270274 A270275 A270276 A270277
139 1,5,5,33,13,93,33 A270278 A270279 A270280 A270281
141 1,8,4,40,17,108,17 A270282 A270283 A270284 A270285
145,153 1,4,5,32,4,101,20 A270286 A270287 A270288 A270289
147 1,5,5,37,4,105,20 A270290 A270291 A270292 A270293
149 1,8,4,44,5,116,12 A270317 A270318 A270319 A270320
150 1,5,8,20,20,44,3 A270321 A270322 A270323 A270324
155 1,5,5,37,8,97,25 A270325 A270326 A270327 A270328
157 1,8,4,44,5,116,12 A270329 A270330 A270331 A270332
158 1,5,12,20,32,32,64 A270333 A270334 A270335 A270336
161 1,4,9,24,29,64,49 A270450 A270451 A270452 A270453
163,171,227,235 1,5,9,33,25,85,49 A270454 A270222 A270455 A270456
165 1,8,4,40,17,104,20 A270457 A270458 A270459 A270460
169 1,4,9,24,29,68,41 A270461 A270462 A270463 A270464
173 1,8,4,40,17,112,20 A270465 A270466 A270467 A270468
177 1,4,9,32,33,84,65 A270618 A270619 A270620 A270621
179 1,5,9,41,21,93,41 A270622 A270623 A270624 A270625
181 1,8,4,44,9,108,21 A270626 A270627 A270628 A270629
182 1,5,8,20,32,36,52 A270630 A270631 A270632 A270633
185 1,4,9,32,33,92,65 A270634 A270635 A270636 A270637
187 1,5,9,41,21,93,49 A270673 A270674 A270675 A270676
189 1,8,4,44,9,108,21 A270677 A270678 A270679 A270680
190,254 1,5,12,24,32,52,60 A270681 A270682 A270683 A270684
193 1,4,9,24,21,72,45 A270685 A270686 A270687 A270688
195 1,5,5,33,13,93,25 A270689 A270690 A270691 A270692
197 1,8,4,40,17,100,25 A270716 A270717 A270718 A270719
201 1,4,9,28,17,80,28 A270720 A270721 A270722 A270723
203 1,5,5,33,13,93,33 A270725 A270726 A270727 A270728
205 1,8,4,40,17,108,17 A270729 A270730 A270731 A270732
206 1,5,8,20,20,32,48 A270733 A270734 A270735 A270736
209 1,4,9,28,25,80,53 A270891 A270892 A270893 A270894
211 1,5,5,37,4,105,20 A270897 A270898 A270899 A270900
213 1,8,4,44,9,112,21 A270901 A270902 A270903 A270904
214 1,5,8,24,20,60,28 A270905 A270906 A270907 A270908
217 1,4,9,32,9,96,44 A270909 A270910 A270911 A270912
219 1,5,5,37,8,97,25 A270930 A270931 A270932 A270933
221 1,8,4,44,9,116,9 A270934 A270935 A270936 A270937
222 1,5,12,20,32,32,72 A270938 A270939 A270940 A270941
225 1,4,13,28,33,84,61 A270942 A270943 A270944 A270945
229 1,8,4,40,17,104,20 A270946 A270947 A270948 A270949
233 1,4,13,32,21,68,40 A270976 A270977 A270978 A270979
237 1,8,4,40,17,112,20 A270980 A270981 A270982 A270983
238 1,5,8,20,20,32,48 A270984 A270985 A270986 A270987
241 1,4,13,36,37,88,77 A270988 A270989 A270990 A270991
243 1,5,9,41,21,101,49 A269702 A271001 A271002 A271003
245 1,8,4,44,13,112,25 A271004 A271005 A271006 A271007
246 1,5,8,24,28,48,36 A271008 A271009 A271010 A271011
249 1,4,13,40,25,88,81 A271012 A271013 A271014 A271015

2D 5-Neighbor Outer Totalistic Cellular Automata Sequences in the OEIS (continued)
Rule Sequence ON ON(2^n-1) Partial Sum First Diff
251 1,5,9,41,21,101,49 A271016 A271017 A271018 A271019
253 1,8,4,44,13,116,13 A271051 A270935 A271052 A271053
259 1,5,5,36,5,108,5 A271054 A271055 A271056 A271057
260,268,292,300,388,396,420,428,772,780,804,812,900,908,932,940 1,4,5,12,4,16,20 A253086 A253087 A255150 A271059
261,269,277,285,293,301,309,317,325,333,341,349,357,365,373,381 1,8,1,48,1,120,1 A271060 A271061 A271062 A271064
262 1,5,4,20,9,33,13 A271065 A271066 A271067 A271068
267 1,5,5,40,13,100,13 A271083 A271084 A271085 A271086
270 1,5,8,21,20,28,36 A271087 A271088 A271089 A271090
275 1,5,5,40,5,112,5 A271091 A271092 A271093 A271094
276,284,308,316,340,348,372,380,404,412,436,444,468,476,500,508, 788,796,820,828,852,860,884,892,916,924,948,956,980,988,1012,1020 1,4,9,16,25,36,49 A000290* A000302 A000330* A005408*
278 1,5,8,20,16,44,32 A271095 A271096 A271097 A271098
283 1,5,5,44,5,109,16 A271117 A271118 A271119 A271120
286 1,5,12,17,37,28,76 A271121 A271122 A271123 A271124
289 1,4,5,32,9,92,21 A271125 A271126 A271127 A271128
291 1,5,9,32,9,101,41 A271129 A271130 A271131 A271132
294 1,5,4,20,9,33,17 A271133 A271136 A271134 A271135
297 1,4,5,32,13,88,17 A271148 A271149 A271150 A271151
299 1,5,9,32,9,101,45 A271152 A271153 A271154 A271155
302 1,5,8,21,24,37,44 A271156 A271157 A271158 A271159
305 1,4,5,32,9,100,21 A271160 A271161 A271162 A271163
307 1,5,9,32,13,104,25 A271164 A271165 A271166 A271167
310 1,5,8,20,28,40,45 A271195 A271196 A271198 A271199
313 1,4,5,32,13,88,21 A271200 A271201 A271202 A271203
315 1,5,9,32,13,104,25 A266206 A270565 A271248 A271249
318 1,5,12,21,37,40,68 A271250 A271251 A271252 A271253
323 1,5,5,36,9,96,17 A270565 A271254 A271255 A271256
324,332,356,364,452,460,484,492,836,844,868,876,964,972,996,1004 1,4,5,12,8,24,25 A246316 A246317 A271257 A271258
326 1,5,4,20,9,37,24 A271259 A271260 A271261 A271262
329 1,4,5,40,9,100,5 A265689 A271274 A271275 A271276
331 1,5,5,40,13,100,21 A271277 A271278 A271279 A271280
334 1,5,8,21,20,32,44 A271281 A271282 A271283 A271284
337 1,4,5,40,9,100,21 A271285 A271286 A271287 A271288
339 1,5,5,40,9,100,25 A271289 A271290 A271291 A271292
342 1,5,8,24,17,53,32,96 A264797 A270126 A269511 A269512
345 1,4,5,44,5,104,13 A271293 A271294 A271295 A271296
347 1,5,5,44,5,109,16 A271297 A271298 A271299 A271300
350 1,5,12,17,37,28,76 A271301 A271302 A271303 A271304
353 1,4,9,32,13,84,21 A271305 A271306 A271307 A271308
355 1,5,9,32,17,101,36 A271397 A271398 A271399 A271408
358 1,5,4,20,9,37,24 A271409 A271411 A271412 A271413
361 1,4,9,32,13,92,45 A271414 A271415 A271416 A271417
363 1,5,9,32,17,101,40 A264099 A268153 A268154 A268194
366 1,5,8,21,24,37,52 A268195 A268202 A268275 A268276
369 1,4,9,32,17,92,37 A268277 A268282 A268503 A270793
371 1,5,9,32,21,96,41 A271454 A271455 A271456 A271457
374 1,5,8,24,25,53,36 A169701 A271458 A271459 A271460
377 1,4,9,32,17,104,29 A271461 A271462 A271463 A271464
379 1,5,9,32,21,96,41 A265916 A270423 A271537 A271538
382 1,5,12,21,37,40,76 A271539 A271540 A271541 A271542
387 1,5,9,24,17,84,41 A271543 A271544 A271545 A271546
389 1,8,5,40,17,104,17 A271594 A271595 A271596 A271597
390 1,5,4,20,9,33,13 A271598 A271599 A271600 A271601
393 1,4,5,28,9,84,29 A271602 A271603 A271604 A271605
395 1,5,9,28,17,89,32 A271685 A271686 A271687 A271688
397 1,8,5,44,17,108,33 A271689 A271690 A271691 A271692
398 1,5,8,21,20,28,36 A271693 A271694 A271695 A271696
401,409 1,4,5,32,5,96,17 A271803 A271804 A271805 A271806
403 1,5,9,28,17,96,45 A271807 A271808 A271809 A271810
405 1,8,5,44,5,116,17 A271812 A271813 A271814 A271815
406 1,6,14,34,54,102,139 A271885 A271887 A271772 A271888
411 1,5,9,32,25,93,48 A271889 A271890 A271891 A271892
413,445,477,509 1,8,5,48,5,120,5 A272007 A271061 A272009 A272010
414 1,5,12,21,32,40,81 A272012 A272013 A272014 A272015
417 1,4,9,28,17,68,41 A272016 A272017 A272018 A272019
419 1,5,13,28,25,101,56 A272045 A272046 A272047 A272048
421 1,8,5,40,17,108,29 A272049 A272050 A272051 A272052
422 1,5,4,20,9,33,17 A272085 A272086 A272087 A272088
425 1,4,9,28,17,68,41 A272089 A272218 A272091 A272092
427 1,5,13,32,37,89,80 A271902 A271903 A271904 A272110
429 1,8,5,44,17,108,33 A272111 A272112 A272113 A272114
430 1,5,8,21,24,37,44 A272115 A002450* A272116 A272117
433 1,4,9,36,25,88,65 A272145 A272146 A272147 A272148
435 1,5,13,36,33,92,65 A272149 A272150 A272151 A272152
437 1,8,5,44,9,112,21 A272153 A272154 A272155 A272156
438 1,5,8,20,32,40,36 A272217 A272218 A272219 A272220
441 1,4,9,36,25,96,65 A272221 A272222 A272223 A272224
443 1,5,13,40,25,97,72 A272225 A272226 A272227 A272228
446 1,5,12,25,28,52,64 A272194 A272249 A272250 A272251
449 1,4,9,24,21,72,45 A272252 A272253 A272254 A272255
451 1,5,9,24,21,72,45 A272256 A272257 A272258 A270844
453 1,8,5,40,17,104,29 A272273 A272274 A272275 A272276
454 1,5,4,20,9,37,28 A246326 A272277 A272278 A272279
457 1,4,9,28,21,92,57 A272280 A272281 A2722782 A272283
459 1,5,9,28,25,81,32 A272287 A272288 A272289 A272290
461 1,8,5,44,17,112,21 A272291 A272292 A272293 A272294
462 1,5,8,21,20,32,48 A246330 A272310 A272311 A272312
465 1,4,9,28,25,84,49 A272313 A272218 A272316 A272317
467 1,5,9,28,29,80,53 A272315 A272319 A272320 A272321
469 1,8,5,44,9,112,21 A272416 A272417 A272418 A272419
470 1,5,8,24,21,56,32 A253078 A272420 A272421 A272422
473 1,4,9,32,21,100,41 A272423 A272424 A272425 A272426
475 1,5,9,32,29,84,61 A272447 A272448 A272449 A272450
478 1,5,12,21,32,44,73 A272451 A272452 A272453 A272454
481 1,4,13,28,33,84,69 A272455 A272456 A272457 A272458
483 1,5,13,28,37,85,76 A248860 A267828 A267829 A272346
485 1,8,5,40,17,108,37 A272350 A272396 A272504 A272505
486 1,5,4,20,9,37,28 A272506 A272507 A272508 A272509
489 1,4,13,32,33,100,65 A272510 A272511 A272512 A272513

2D 5-Neighbor Outer Totalistic Cellular Automata Sequences in the OEIS (continued)
Rule Sequence ON ON(2^n-1) Partial Sum First Diff
491 1,5,13,32,41,76,77 A272539 A272540 A272541 A272542
493 1,8,5,44,17,112,29 A272543 A272544 A272545 A272546
494 1,5,8,21,24,37,52 A169705 A272547 A272548 A169706
497 1,4,13,36,37,88,85 A272556 A272557 A272558 A272559
499 1,5,13,36,37,88,85 A272560 A272561 A272562 A272563
501 1,8,5,44,13,112,25 A272564 A271005 A272566 A272567
502 1,5,8,24,29,48,56 A272577 A272578 A272579 A272580
505 1,4,13,40,29,100,69 A272581 A271286 A272583 A272584
507 1,5,13,40,29,100,69 A272585 A272586 A272587 A272588
510 1,5,12,25,28,56,56 A169699 A092440 A272700 A169700
513,769 1,4,13,24,53,65,113 A272702 A059153 A272703 A272704
515,523 1,5,13,25,49,69,109 A272705 A272706 A272707 A272708
517 1,8,20,37,60,84,129 A272730 A272731 A272732 A272733
518,550,582,614 1,5,5,17,5,25,17 A072272 A007483 A253908 A170878
519,527,535,543,551,559,567,575,583,591,599,607,615,623,631,639,647, 655,663,671,679,687,695,703,711,719,727,735,743,751,759,767,775,783, 791,799,807,815,823,831,839,847,855,863,871,879,887,895,903,911,919, 927,935,943,951,959,967,975,983,991,999,1007,1015,1023 1,9,25,49,81,121,169 A016754 A060867 A000447* A008590*
521 1,4,13,24,53,69,105 A272734 A272735 A272736 A272737
525 1,8,20,37,60,84,129 A272738 A272739 A272740 A272741
526 1,5,9,17,17,33,45 A272742 A272743 A272744 A272745
529 1,4,13,28,49,77,96 A272746 A272747 A272748 A272749
531 1,5,13,29,49,89,97 A272750 A272751 A272752 A272753
533 1,8,20,37,64,84,141 A272782 A272783 A272784 A272785
534 1,5,9,21,17,49,29 A272786 A272787 A272788 A272789
537 1,4,13,28,49,81,88 A272790 A272791 A272792 A272793
539 1,5,13,29,49,89,105 A272801 A272802 A272803 A272804
541 1,8,20,37,64,84,141 A272805 A272806 A272807 A272808
542 1,5,13,21,33,37,69 A272809 A272810 A272811 A272812
545 1,4,17,28,57,84,117 A272834 A272835 A272836 A272837
547 1,5,17,29,61,89,121 A272838 A272839 A272840 A272841
549 1,8,20,41,60,97,132 A272842 A272843 A272844 A272845
553 1,4,17,28,57,84,125 A272846 A272218 A272848 A272849
555,571 1,5,17,29,61,89,129 A272920 A272921 A272922 A272923
557 1,8,20,41,60,97,132 A272924 A272925 A272926 A272927
558,686 1,5,9,21,25,37,49 A147562* A002450* A272928 A147582*
561 1,4,17,28,61,89,121 A272769 A272936 A272937 A272938
563 1,5,17,29,61,89,121 A272939 A272940 A272941 A272942
565 1,8,20,41,60,101,137 A272943 A272944 A272945 A272946
566 1,5,9,21,29,37,49 A272986 A272987 A272989 A272990
569 1,4,17,28,61,93,133 A272991 A272992 A272993 A272994
573 1,8,20,41,60,101,141 A272995 A272996 A272997 A272998
574,638,702,766,830,894,958,1022 1,5,13,25,41,61,85 A001844 A092440 A005900* A008586*
577 1,4,17,25,52,73,113 A273022 A273023 A273024 A273025
579 1,5,13,29,57,73,121 A273026 A273027 A273028 A273029
581 1,8,20,41,57,96,116 A273069 A273070 A273071 A273072
585 1,4,17,29,49,81,133 A273073 A273074 A273075 A273076
587 1,5,13,29,57,73,121 A273077 A273078 A273079 A273080
589 1,8,20,41,61,93,129 A273111 A273112 A273113 A273114
590 1,5,9,17,17,37,49 A273115 A273116 A273117 A273118
593 1,4,17,25,60,65,137 A273119 A273120 A273121 A273122
595 1,5,13,33,49,93,97 A272161 A273141 A273142 A273143
597 1,8,20,41,57,104,116 A273144 A273145 A273146 A273147
598 1,5,9,21,17,53,41 A273150 A002450* A273151 A273152
601 1,4,17,29,61,73,132 A272330 A272373 A272824 A272825
603 1,5,13,33,49,93,105 A272828 A272833 A273173 A273174
605 1,8,20,41,61,105,125 A273175 A273176 A273177 A273178
606 1,5,13,21,33,37,77 A273204 A273205 A273206 A273207
609 1,4,21,29,72,84,141 A273208 A273209 A273210 A273211
611 1,5,17,37,61,97,133 A273212 A273213 A273214 A273215
613 1,8,20,45,61,112,132 A273241 A273242 A273243 A273244
617 1,4,21,29,72,88,152 A273246 A273247 A273248 A273249
619,635 1,5,17,37,65,101,137 A273250 A273251 A273252 A273253
621 1,8,20,45,61,112,136 A273266 A273267 A273268 A273269
622 1,5,9,21,25,37,57 A269522 A269566 A269567 A269568
625 1,4,21,29,72,84,141 A273270 A273271 A273272 A273273
627 1,5,17,37,61,101,121 A273274 A273275 A273276 A273277
629 1,8,20,45,61,112,132 A273295 A273296 A273297 A273298
630 1,5,9,21,29,45,65 A269523 A267268 A269543 A269629
633 1,4,21,29,72,88,156 A273299 A273300 A273301 A273303
637 1,8,20,45,61,112,136 A273304 A273305 A273306 A273307
641,649,897,905 1,4,17,40,73,112,161 A273309 A273310 A273311 A273312
643,651,707,715 1,5,17,41,73,113,161 A166147* A273313 A273314 A273315
645,653,661,669,677,685,693,701,709,717,725,733,741,749,757,765 1,8,24,48,80,120,168 A033996* A271061 A273316 A008590*
646 1,5,5,17,9,29,17 A273326 A273327 A273328 A273329
654 1,5,9,17,21,29,37 A273330 A273331 A273332 A273333
657,665 1,4,17,48,80,120,168 A273334 A273335 A273336 A273337
659,667,723,731 1,5,17,49,81,121,169 A273384 A273385 A273386 A273387
662 1,5,9,21,21,45,33 A273388 A273389 A273390 A273391
670 1,5,13,21,33,49,61 A273392 A273393 A273394 A273395
673,681,689,697 1,4,21,44,77,116,165 A273405 A269907 A273406 A273407
675,683,691,699,739,747,755,763 1,5,21,45,77,117,165 A078371* A269911 A273408 A234275*
678 1,5,5,17,9,29,21 A079317 A052539* A273409 A151921
694 1,5,9,21,33,45,53 A273410 A272832 A273411 A273412
705,713 1,4,21,41,72,113,160 A273417 A273418 A273419 A273420
710 1,5,5,17,9,29,17 A273421 A273422 A273423 A273424
718 1,5,9,17,21,29,37 A273425 A273426 A273427 A273428
721,729 1,4,21,41,80,120,168 A273443 A273446 A273447 A273448
726 1,5,9,21,21,53,53 A273449 A273450 A273451 A273452
734 1,5,13,21,33,49,61 A273453 A273454 A273455 A273456
737,745,753,761,993,1001,1009,1017 1,4,25,49,81,121,169 A016754* A060867* A273480 A273481
742 1,5,5,17,9,29,21 A273482 A273483 A273484 A273485
750 1,5,9,21,25,37,57 A169707 A002450* A253098 A169708
758 1,5,9,21,33,45,61 A273486 A273489 A273490 A273491
771,787,835,851 1,5,17,33,65,89,137 A273499 A272022 A273500 A273501
773,781,789,797,837,845,853,861 1,8,21,40,65,96,133 A000567* A165665 A002414 A016921*
774 1,5,5,17,5,25,17 A273502 A273503 A273504 A273505
777 1,4,13,24,53,69,105 A273414 A273444 A273532 A273533
779,795,843,859 1,5,17,37,61,97,125 A273538 A273539 A273540 A273541
782 1,5,9,17,17,33,53 A273534 A273535 A273536 A273537
785 1,4,13,28,49,77,104 A273557 A273558 A273559 A273560
790,854 1,5,9,25,29,53,49 A273561 A092440 A273562 A273563
793 1,4,13,28,49,81,108 A273564 A273565 A273566 A273567

2D 5-Neighbor Outer Totalistic Cellular Automata Sequences in the OEIS (concluded)
Rule Sequence ON ON(2^n-1) Partial Sum First Diff
798,862 1,5,13,21,37,41,85 A273569 A273570 A273571 A273572
801 1,4,17,28,57,84,117 A273573 A273574 A273575 A273576
803,811,819,827,867,875,883,891 1,5,21,33,77,105,153 A273577 A270222 A273578 A273579
805,821,869,885 1,8,21,44,69,113,145 A273602 A273603 A273604 A273605
806 1,5,5,17,5,25,17 A273606 A273607 A273608 A273609
809 1,4,17,28,57,84,125 A273610 A273611 A273612 A273613
813,829,877,893 1,8,21,44,69,117,153 A258448 A273639 A273640 A273641
814 1,5,9,21,29,41,53 A273642 A273643 A273644 A273645
817 1,4,17,28,61,89,121 A273646 A273647 A273648 A273649
822,886 1,5,9,25,37,49,57 A269918 A272762 A272847 A273370
825 1,4,17,28,61,93,141 A273430 A273431 A273581 A273674
833,849 1,4,17,33,56,85,120 A273675 A273676 A273677 A273678
838 1,5,5,17,5,25,17 A273544 A273680 A273681 A273682
841,857 1,4,17,37,61,97,124 A273683 A273684 A273685 A273686
846 1,5,9,17,17,37,53 A273687 A273688 A273689 A273690
865,881 1,4,21,33,68,105,140 A273699 A273700 A273701 A273702
870 1,5,5,17,5,25,17,61 A273703 A273704 A273705 A273706
873,889 1,4,21,33,68,105,144 A273707 A273708 A273709 A273710
878 1,5,9,21,29,41,61,65 A273739 A273740 A273741 A273742
899,907,915,923,963,971,979,987 1,5,21,45,77,117,165 A265056 A269911 A273408 A234275*
901,909,917,925,933,941,949,957,965,973,981,989,997,1005,1013,1021 1,8,25,49,81,121,169 A273743 A270007 A273744 A273745
902 1,5,5,17,9,29,17 A273758 A273759 A273760 A273761
910 1,5,9,17,21,29,37 A273762 A273763 A273764 A273765
913,921 1,4,17,48,81,121,169 A273766 A273767 A273768 A273769
918,982 1,5,9,25,29,53,53 A273746 A273747 A273748 A273749
926,990 1,5,13,21,37,45,77 A273750 A002450* A273778 A273779
929,937,945,953 1,4,21,48,81,121,169 A273780 A273767 A273781 A273782
931,939,947,955,995,1003,1011,1019 1,5,25,49,81,121,169 A273789 A273385 A273790 A273791
934 1,5,5,17,9,29,21 A273792 A273793 A273794 A273795
942 1,5,9,21,29,41,53 A169649* A273796 A273797 A169648*
950,1014 1,5,9,25,37,53,65 A273827 A273828 A273829 A273830
961,977 1,4,21,45,76,117,164 A273831 A273832 A273833 A273834
966 1,5,5,17,9,29,17 A273835 A273836 A273837 A273838
969,985 1,4,21,45,76,121,169 A273847 A273848 A273849 A273850
974 1,5,9,17,21,29,37 A273851 A273852 A273853 A273854
998 1,5,5,17,9,29,21 A273855 A273856 A273857 A273858
1006 1,5,9,21,29,41,61 A169709 A273860 A273861 A169710

## Sequences in the OEIS Related to 2D 5-Neighbor Outer Totalistic Cellular Automata Related to the Position of ON Cells Along the X-Axis

```Column headings in the table below:

Rule      Wolfram's Rule Number(s)
Left(B)   Sequence describing the binary representation of the x-axis from the left edge to the origin
Right(B)  Sequence describing the binary representation of the x-axis from the origin to the right edge
Left(D)   Sequence describing the decimal representation of the x-axis from the left edge to the origin
Right(D)  Sequence describing the decimal representation of the x-axis from the origin to the right edge
(an asterisk, "*", in an A-number indicates a near match)
```

2D 5-Neighbor Outer Totalistic Cellular Automata Sequences in the OEIS
Rule Left(B) Right(B) Left(D) Right(D)
0,8,16,24,32,40,48,56,64,72,80,88,96,104,112,120,128,136,144, 152,160,168,176,184,192,200,208,216,224,232,240,248,256,264,272, 280,288,296,304,312,320,328,336,344,352,360,368,376,384,392,400, 408,416,424,432,440,448,456,464,472,480,488,496,504,512,520,528, 536,544,552,560,568,576,584,592,600,608,616,624,632,640,648,656, 664,672,680,688,696,704,712,720,728,736,744,752,760,768,776,784, 792,800,808,816,824,832,840,848,856,864,872,880,888,896,904,912, 920,928,936,944,952,960,968,976,984,992,1000,1008,1016 A000007 A000007 A000007 A000007
1,9,17,25,257,265,273,281 A277797 A277798 A277799 A277800
2,10,18,26,34,42,50,58,66,74,82,90,98,106,114,122,130,138,146, 154,162,170,178,186,194,202,210,218,226,234,242,250,258,266,274, 282,290,298,306,314,322,330,338,346,354,362,370,378,386,394,402, 410,418,426,434,442,450,458,466,474,482,490,498,506,514,522,530, 538,546,554,562,570,578,586,594,602,610,618,626,634,642,650,658, 666,674,682,690,698,706,714,722,730,738,746,754,762,770,778,786, 794,802,810,818,826,834,842,850,858,866,874,882,890,898,906,914, 922,930,938,946,954,962,970,978,986,994,1002,1010,1018 A000012 A011557 A000012 A000079
3,11,19,27,67,75,83,91 A277864 A277865 A277866 A277867
4,12,36,44,68,76,84,92,100,108,116,124,132,140,164,172,196,204, 212,220,228,236,244,252,516,524,548,556,580,588,596,604,612,620, 628,636,644,652,676,684,708,716,724,732,740,748,756,764 A277916 A277917 A277918 A101692*
5,13,21,29,37,45,53,61,69,77,85,93,101,109,117,125 A277926 A277927 A277928 A277929
6,38,70,86,102,134,166,198,230 A277931 A277932 A277933 A277934
7,15,23,31,39,47,55,63,71,79,87,95,103,111,119,127,135,143,151,

159,167,175,183,191,199,207,215,223,231,239,247,255,263,271,279, 287,295,303,311,319,327,335,343,351,359,367,375,383,391,399,407, 415,423,431,439,447,455,463,471,479,487,495,503,511

A277560 A277560 A277736 A277936
14,46,110,142,174,190,238,254 A277952 A277953 A277954 A277955
20,28,52,60,148,156,180,188,532,540,564,572,660,668,692,700 A273495 A273531 A273972 A273973
22 A274060 A274216 A274224 A274473
30 A274474 A274475 A274476 A274487
33 A276708 A276768 A276966 A277773
35 A278343 A278344 A278345 A278346
41 A278421 A278422 A278423 A278424
43,59 A278443 A278444 A278445 A278446
49 A278466 A278467 A278468 A278469
51 A278592 A278593 A278594 A278595
54 A278598 A278599 A278600 A278601
57 A278659 A278660 A278661 A278662
62 A278664 A278665 A278666 A278667
65,81,321,337 A278753 A278754 A278755 A278756
73,89 A278757 A278758 A278759 A278760
78 A278786 A278778 A278788 A278789
94 A278819 A278820 A278821 A278822
97 A278864 A278865 A278866 A278867
99 A278870 A278871 A278872 A278873
105 A278719 A278739 A278859 A278863
107 A278898 A278899 A278900 A278901
113 A278904 A278905 A278292 A278906
115 A278915 A278916 A278917 A278918
118 A278951 A278952 A278953 A278954
121 A278955 A278956 A278957 A278958
123 A278980 A279016 A279023 A279025
126 A272609 A273979 A274059 A274993
129,385 A279028 A279029 A279030 A279031
131,139,163,171,187,227,235,251 A279053 A056830* A052992 A000975
133 A279137 A279138 A279139 A279140
137 A279141 A279142 A279143 A279144
141 A279145 A279146 A279147 A279148
145,153 A279149 A278584 A279150 A279151
147 A279173 A279174 A279175 A279176
150 A279246 A279247 A279248 A279249
155 A279250 A279251 A279252 A279253
157 A279468 A279469 A279470 A279471
158 A279472 A279473 A279474 A279475
161 A279498 A279499 A279500 A279501
165 A279502 A279503 A279504 A279505
169 A279545 A279546 A279547 A279548
173 A279597 A279598 A279599 A279600
177 A279601 A279602 A279603 A279604
179 A279528 A279665 A279666 A279668
181 A279669 A279670 A279671 A279672
182 A279694 A279695 A279696 A279697
185 A279698 A279699 A279700 A279701
189 A279716 A279717 A279718 A279719
193 A279720 A279721 A279722 A279723
195 A279748 A279749 A279750 A279751
197 A279752 A279753 A279754 A279755
201 A279799 A279800 A279801 A279802
203 A279808 A279809 A279810 A279811
205 A279822 A279823 A279824 A279825
206 A279826 A279827 A279828 A279829
209,465 A279118 A279118 A279872 A279872
211 A279873 A279874 A279875 A279876
213,245 A279877 A279878 A279879 A279880
214 A279936 A279937 A279938 A279939
217 A279940 A279941 A279942 A279943
219 A279057 A279123 A279957 A279958
221,253 A279959 A279960 A279961 A279962
222 A279949 A279985 A279986 A279987
225 A279988 A279989 A279990 A279991
229 A279992 A279993 A279994 A279995
233 A279996 A279997 A279998 A279999
237 A280137 A280138 A280139 A280140
241 A280141 A280142 A280143 A280144
243 A280145 A280146 A280147 A280148
246 A280329 A280330 A280331 A280332
249 A280334 A280335 A280336 A280337

2D 5-Neighbor Outer Totalistic Cellular Automata Sequences in the OEIS (continued)
Rule Left(B) Right(B) Left(D) Right(D)
259,275 A280367 A280368 A280369 A280370
260,268,292,300,388,396,420,428,772,780,804,812,900,908,932,940 A280371 A280372 A280373 A280374
261,269,277,285,293,301,309,317,325,333,341,349,357,365,373,381 A280410 A280411 A280412 A051049
262 A280413 A280414 A280415 A280416
267 A280459 A280460 A280461 A280462
270 A280463 A280464 A280465 A280466
276,284,308,316,340,348,372,380,404,412,436,444,468,476,500,508, 773,781,788,789,796,797,820,828,837,845,852,853,860,861,884,892 ,916,924,948,956,980,988,1012,1020 A056830 A279053 A000975 A052992
278 A280365 A280524 A280525 A280526
283 A280527 A280528 A280529 A280530
286 A280561 A280562 A280563 A280564
289 A276708 A276768 A276966 A277773
291 A280565 A280566 A280567 A280568
294,422 A280606 A280607 A280608 A280609
297 A280612 A280613 A280614 A280615
299 A280833 A280834 A280835 A280836
302 A280837 A280838 A280839 A280840
305 A280973 A280974 A280975 A280976
307 A280977 A280978 A280979 A280980
310 A281035 A281036 A281037 A281038
313 A281039 A281040 A281041 A281042
315 A281043 A281044 A281045 A281046
318 A281088 A281099 A281100 A281101
323,339 A278753* A278754* A278755* A278756*
324,332,356,364,452,460,484,492,836,844,868,876,964,972,996,1004 A281102 A281103 A281104 A281105
326 A281106 A281107 A281108 A281109
329 A281172 A281173 A281174 A281175
331 A281176 A281177 A281178 A281179
334 A280099 A280165 A281212 A281213
342 A281214 A281215 A281216 A281217
345 A281218 A281219 A281220 A281221
347 A281277 A281278 A281279 A281280
350 A281281 A281282 A281283 A281284
353 A281285 A281286 A281287 A281288
355 A281304 A281305 A281306 A281307
358 A281308 A281309 A281310 A281311
361 A281410 A281411 A281412 A281413
363 A281414 A281415 A281416 A281417
366 A281418 A281419 A281420 A281421
369 A281514 A281515 A281516 A281517
371 A281518 A281519 A281520 A281521
374 A281522 A281523 A281524 A281525
377 A281628 A281629 A281630 A281631
379 A281632 A281633 A281634 A281635
382 A281636 A281637 A281638 A281639
387 A281670 A281671 A281672 A281673
389 A281674 A281675 A281676 A281677
390 A281735 A281736 A281737 A281738
393 A281739 A281740 A281741 A281742
395 A281748 A281749 A281750 A281751
397 A281752 A281753 A281754 A281755
398 A281756 A281757 A281758 A281759
401,409,425 A281840 A281841 A281842 A281843
403 A281844 A281845 A281846 A281847
405 A281848 A281849 A281850 A281851
406 A281095 A281096 A281892 A281893
411 A281894 A281895 A281896 A281897
413,445,477,509 A282002 A282003 A282004 A282005
414 A282006 A282007 A282008 A282009
417 A282065 A282066 A282067 A282068
419 A282069 A282070 A282071 A282072
421 A282073 A282074 A282075 A282076
427 A282103 A282104 A282105 A282106
429 A282117 A282118 A282119 A282120
430 A282121 A282122 A282123 A282124
433 A282199 A282200 A282201 A282202
435 A282203 A282204 A282205 A282206
437 A282214 A282215 A282216 A282217
438 A282218 A282219 A282220 A282221
441 A282222 A282223 A282224 A282225
443 A282257 A282258 A282259 A282260
446 A282261 A282262 A282263 A282264
449 A282265 A282266 A282267 A282268
451 A282295 A282297 A282298 A282299
453 A282300 A282301 A282302 A282303
454 A282305 A282306 A282307 A282308

2D 5-Neighbor Outer Totalistic Cellular Automata Sequences in the OEIS (continued)
Rule Left(B) Right(B) Left(D) Right(D)
457 A282359 A282360 A282361 A282362
459 A282363 A282364 A282365 A282366
461 A282367 A282368 A282369 A282370
462,510 A282385 A282386 A282387 A282388
467 A282411 A282412 A282413 A282414
469,501 A282415 A282416 A282417 A282418
470 A282419 A282420 A282421 A282422
473 A282447 A282428 A282429 A282450
475 A282451 A282452 A282453 A282454
478 A282482 A282483 A282484 A282485
481 A282486 A282487 A282488 A282489
483 A282490 A282491 A282492 A282493
485 A282276 A282325 A282514 A282553
486 A282602 A282603 A282604 A282605
489 A282606 A282607 A282608 A282609
491 A282652 A282653 A282654 A282655
493 A282656 A282657 A282658 A282659
494 A282660 A282661 A282662 A282663
497 A282674 A282675 A282676 A282677
499 A282678 A282679 A282680 A282681
502 A282682 A282683 A282684 A282685
505 A282796 A282797 A282798 A282799
507 A282800 A282801 A282802 A282803
513,561,769,817 A282804 A282805 A282806 A282807
515,523,547,555,571 A279053* A281146 A052992* A153772*
517 A281730 A282510 A282825 A282599
518,550,582,598,614 A273912 A273910 A038185 A273911
519,527,535,543,551,558,559,567,574,575,583,591,599,607,615,622,

623,631,638,639,647,655,663,671,679,686,687,695,702,703,711,719, 727,735,743,750,751,759,766,767,775,783,791,799,807,814,815,823, 830,831,839,847,855,863,871,878,879,887,894,895,903,911,919,927, 935,942,943,951,958,959,967,975,983,991,999,1006,1007,1015,1022, 1023

A002275* A002275* A000225* A000225*
521 A282826 A282827 A282828 A282829
525 A282907 A282908 A282909 A282910
526 A282911 A282912 A282913 A282914
529,785 A282915 A282916 A282917 A282918
531 A282950 A282951 A282952 A282953
533 A282954 A282955 A282956 A282957
534 A282958 A282959 A282960 A282961
537 A282976 A282977 A282978 A282979
539 A282980 A282981 A282982 A282983
541 A282984 A282985 A282986 A282987
542 A283005 A283006 A283007 A283008
545 A283009 A283010 A283011 A283012
549 A283013 A283014 A283015 A283016
553 A282088 A282142 A282577 A282579
557 A282580 A282638 A282776 A283043
563 A283044 A283045 A283046 A283047
565 A283057 A283058 A283059 A283060
566 A283061 A283062 A283063 A283064
569 A283065 A283066 A283067 A283068
573 A283079 A283080 A283081 A283082
577 A283083 A283084 A283085 A283086
579 A283087 A283088 A283089 A283090
581 A283132 A283133 A283134 A283135
585 A283136 A283137 A283138 A283139
587 A283140 A283141 A283142 A283143
589 A283171 A283172 A283173 A283174
590 A283175 A283176 A283177 A283178
593 A283179 A283180 A283181 A283182
595 A283210 A283211 A283212 A283213
597 A283214 A283215 A283216 A283217
601 A283218 A283219 A283220 A283221
603 A283223 A283249 A283250 A283251
605 A283252 A283253 A283254 A283255
606 A283256 A283257 A283258 A283259
609 A283283 A283284 A283285 A283286
611 A283287 A283288 A283289 A283290
613 A283291 A283292 A283293 A283294
617 A282871 A283348 A283349 A283350
619,635 A283351 A283352 A140252* A283353
621 A283355 A283356 A283357 A283358
625 A283372 A283373 A283374 A283375
627 A283376 A283377 A283378 A283379
629 A283387 A283388 A283389 A283390
630 A283396 A283397 A283398 A283399
633 A283400 A283401 A283402 A283403
637 A283404 A283405 A283406 A283407

2D 5-Neighbor Outer Totalistic Cellular Automata Sequences in the OEIS (concluded)
Rule Left(B) Right(B) Left(D) Right(D)
641,649,673,681,689,697,897,905 A283504 A283505 A283506 A283507
643,651,675,683,691,699,707,715,739,747,755,763 A267623 A283508 A036563 A153893*
645,653,661,669,677,685,693,701,709,717,725,733,741,749,757,765 A105279* A002275* A000918* A000225*
646 A283581 A283582 A283583 A283584
654 A283585 A283586 A283587 A283588
657,665 A283589 A283590 A283591 A283592
659,667,723,731 A283596 A283597 A000225* A000225*
662 A283600 A283601 A283602 A283603
670 A283604 A283605 A283606 A283607
678,742 A283641 A266508 A086893 A283642
694 A283644 A283645 A283646 A283647
705,713 A283648 A283649 A283650 A283651
710 A283699 A283700 A283701 A283702
718 A283703 A283704 A283705 A283706
721,729 A283707 A283708 A283709 A000225*
726 A283815 A283816 A283817 A283818
734 A283849 A283850 A283864 A283865
737,745,753,761,993,1001,1009,1017 A002275* A002275* A000225* A000225*
758 A283712 A283713 A283752 A2837905
771,787,803,811,819,827,835,851,867,875,883,891 A283906 A283907 A283908 A283909
774 A283910 A283911 A283912 A283913
777 A283914 A283915 A283916 A283917
779,795,843,859 A284020 A284021 A284022 A284023
782 A284024 A284025 A284026 A284027
790,822,854,886 A284028 A284029 A283908* A284031
793 A284083 A284084 A284085 A284086
798,862 A284087 A284088 A284022* A284090
801 A284133 A284134 A284135 A284136
805,821,869,885 A284137 A284138 A284139 A284140
806 A284141 A284142 A284143 A284144
809 A284175 A284176 A284177 A284178
813,829,877,893 A284179 A284180 A284181 A284182
825 A284183 A284184 A284185 A284186
833,849 A284235 A284236 A284237 A284238
838 A284239 A284240 A284241 A284242
841,857 A284243 A284244 A284245 A284246
846 A284274 A284296 A284297 A284298
865,881 A284299 A284300 A284301 A284302
870 A284303 A284304 A284305 A284306
873,889 A284347 A284348 A284349 A284350
899,907,915,923,963,971,979,987 A284351 A284352 A284353 A284354
901,909,917,925,933,941,949,957,965,973,981,989,997,1005,1013,1021 A002275* A002275* A000225* A000225*
902 A284355 A284356 A284357 A284358
910 A284399 A284400 A284401 A284402
913,921,929,937,945,953 A284403 A284404 A284405 A284406
918,982 A284407 A284408 A284409 A284410
926,990 A284419 A284420 A284421 A284422
931,939,947,955,995,1003,1011,1019 A002275* A002275* A000225* A000225*
934 A284423 A284424 A284425 A284426
950,1014 A284479 A284480 A284481 A284482
961,977 A284483 A284484 A101622* A284485
966 A284536 A284537 A284538 A284539
969,985 A002275* A002275* A000225* A000225*
974 A284540 A284541 A284542 A284543
998 A284544 A284545 A284546 A284547

## Sequences in the OEIS Related to 2D 5-Neighbor Outer Totalistic Cellular Automata Related to the Position of ON Cells Along the Diagonal

```Column headings in the table below:

Rule    Wolfram's Rule Number(s)
In(B)   Sequence describing the binary representation of the diagonal from a corner to the origin
Out(B)  Sequence describing the binary representation of the diagonal from the origin to a corner
In(D)   Sequence describing the decimal representation of the diagonal from a corner to the origin
Out(D)  Sequence describing the decimal representation of the diagonal from the origin to a corner
(an asterisk, "*", in an A-number indicates a near match)
```

2D 5-Neighbor Outer Totalistic Cellular Automata Sequences in the OEIS
Rule In(B) Out(B) In(D) Out(D)
0,4,8,12,16,24,32,36,40,44,48,56,64,68,72,76,80,88,96,

100,104,108,112,120,128,132,136,140,144,152,160,164,168,172, 176,184,192,196,200,204,208,216,224,228,232,236,240,248,256, 264,272,280,288,296,304,312,320,328,336,344,352,360,368,376, 384,392,400,408,416,424,432,440,448,456,464,472,480,488,496, 504,512,516,520,524,528,536,544,548,552,556,560,568,576,580, 584,588,592,600,608,612,616,620,624,632,640,644,648,652,656, 664,672,676,680,684,688,696,704,708,712,716,720,728,736,740, 744,748,752,760,768,776,784,792,800,808,816,824,832,840,848, 856,864,872,880,888,896,904,912,920,928,936,944,952,960,968, 976,984,992,1000,1008,1016

A000007 A000007 A000007 A000007
1,9,17,25,129,137,257,261,265,269,273,277,281,285,293,301,

309,317,325,333,337,341,345,349,357,365,373,381,385,393,401, 405,409,413,445,465,469,473,477,509

A280410 A280411 A280412 A280413
2,10,18,26,34,42,50,58,66,74,82,90,98,106,114,122,130,138,

146,154,162,170,178,186,194,202,210,218,226,234,242,250,258, 266,274,282,290,298,306,314,322,330,338,346,354,362,370,378, 386,394,402,410,418,426,434,442,450,458,466,474,482,490,498, 506,514,518,522,526,530,538,546,550,554,558,562,570,578,582, 586,590,594,602,610,614,618,622,626,634,642,646,650,654,658, 666,674,678,682,686,690,698,706,710,714,718,722,730,738,742, 746,750,754,762,770,778,786,794,802,810,818,826,834,842,850, 858,866,874,882,890,898,906,914,922,930,938,946,954,962,970, 978,986,994,1002,1010,1018

A000012 A011557 A000012 A000079
3,11,19,27,67,75,83,91 A285473 A285474 A080924 A285475
5,13,21,29,37,45,53,61,69,77,85,93,101,109,117,125 A277926 A277927 A277928 A277928
6,14,38,46,70,78,102,110,134,142,166,174,198,206,230,238 A019590 A285476 A019590 A130706
7,15,23,31,39,47,55,63,71,79,87,95,103,111,119,127,135,

143,151,159,167,175,183,191,199,207,215,223,231,239,247,255, 263,271,279,287,295,303,311,319,327,335,343,351,359,367,375, 383,391,399,407,415,423,431,439,447,455,463,471,479,487,495, 503,511

A277560 A277560 A277936 A277936
20,28,52,60,148,156,180,188,532,540,564,572,660,668,692,

700

A285477 A285478 A285479 A285480
22,86 A285434 A285435 A285436 A285437
30 A285536 A285637 A285538 A285539
33,289 A282415 A282416 A282417 A282418
35,43,59,163,171,227,235 A285540 A285541 A285542 A285543
41 A285544 A285545 A285546 A285547
49 A285556 A285557 A285558 A285559
51 A285560 A285561 A285562 A285563
54 A285608 A285609 A285610 A285611
57 A285604 A285605 A285606 A285607
62 A285612 A285613 A056453 A233411*
65,321 A285643 A285644 A285645 A285646
73 A285647 A285648 A285649 A285650
81 A285651 A285652 A285653 A285654
84,92,116,124,212,220,244,252,596,604,628,636,724,732,756,

764

A285771 A285772 A285773 A285774
89,145,153 A285775 A285776 A285777 A285778
94 A285780 A285781 A285782 A285783
97 A285816 A285817 A285818 A285819
99 A285820 A285821 A285822 A285823
105 A285825 A285826 A285827 A285828
107 A284940 A285833 A285834 A285835
113 A285837 A285838 A285839 A285840
115 A285841 A285842 A285843 A285844
118 A285897 A285907 A285908 A285909
121 A285910 A285911 A285912 A285913
123 A285945 A285946 A285947 A285948
126 A285941 A285942 A285943 A285944
131 A285xxx A285xxx A285xxx A285xxx
133 A286018 A286019 A286020 A286021
139 A286022 A286023 A286024 A286025
141 A286026 A286027 A286028 A286029
147 A286078 A286079 A286080 A286081
149 A286082 A286083 A286084 A286085
150 A286086 A286087 A286088 A286089
155 A286112 A286113 A286114 A286115
157 A286116 A286117 A286118 A286119
158 A286120 A286121 A286122 A286123
161 A286136 A286140 A286165 A286166
165 A286167 A286168 A286169 A286170
169 A286171 A286172 A286173 A286174
173 A286196 A286197 A286198 A286199
177 A286200 A286201 A286202 A286203
179 A286204 A286205 A286206 A286207
181 A286403 A286404 A286405 A286406
182 A286407 A286408 A286409 A286410
185 A286411 A286412 A286413 A286414
187 A286498 A286500 A286501 A286502
189 A286503 A286504 A286505 A286506
190,254 A286507 A286508 A016116 A016116*
193 A286638 A286639 A286640 A286641
195 A286642 A286643 A286644 A286645
197 A286646 A286647 A286648 A286649
201 A286668 A286669 A286670 A286671
203 A286672 A286673 A286674 A286675
205 A286694 A286695 A286696 A286697
209 A286698 A286699 A286700 A286701
211 A286702 A286703 A286704 A286705
213 A286730 A286731 A286732 A286733
214 A286734 A286735 A286736 A286737
217 A286738 A286739 A286740 A286741
219 A286766 A286767 A286768 A286769
221 A286770 A286771 A286772 A286773
222 A286774 A286775 A286776 A286777
225 A286960 A286961 A286962 A286963
229 A283429 A286964 A286965 A286966
233 A286967 A286943 A286968 A286969
237 A287077 A287078 A287079 A287080
241 A287094 A287095 A287096 A287097
243 A287098 A287099 A287100 A287101
245 A287129 A287130 A287131 A287132
246 A287133 A287134 A287135 A287136
249 A287137 A287138 A287139 A287140
251 A286811 A287187 A287188 A287189
253 A287190 A287191 A287192 A287193

2D 5-Neighbor Outer Totalistic Cellular Automata Sequences in the OEIS (continued)
Rule In(B) Out(B) In(D) Out(D)
259 A287194 A287196 A287197 A287199
260,268,292,300,388,396,420,428,772,780,804,812,900,908,932,

940

A287283 A287284 A287285 A287287
262 A287288 A287289 A287290 A287291
267 A287460 A287461 A287462 A287463
270 A287464 A287465 A287466 A287467
275 A280410* A280411* A280412* A051049*
276,284,308,316,340,348,372,380,404,412,436,444,468,476,500,

508,788,796,820,828,852,860,884,892,916,924,948,956,980,988, 1012,1020

A287468 A287469 A077896 A287470
278 A287486 A287487 A287488 A287489
283 A287490 A287491 A287492 A287493
286 A287494 A287495 A287480 A287496
291 A287499 A287500 A287501 A287502
294 A287503 A287504 A287505 A287506
297 A287507 A287508 A287509 A287510
299 A287535 A287536 A287537 A287538
302 A287539 A287540 A287541 A287542
305 A287543 A287544 A287545 A287546
307 A286818 A286818 A287598 A287599
310 A287600 A287602 A287603 A287604
313 A287605 A287606 A287607 A287608
315 A287622 A287623 A287624 A287625
318 A287626 A287627 A287628 A287629
323 A285643* A285644* A285645* A285646*
324,332,356,364,452,460,484,492,836,844,868,876,964,972,996,1004 A287630 A287631 A287632 A287633
326 A287710 A287711 A287712 A287713
329 A287714 A287715 A287716 A287717
331 A287718 A287719 A287720 A287721
334 A287734 A287735 A287736 A287737
339 A287738 A287739 A287740 A287741
342 A287742 A287743 A287744 A287745
347 A287749 A287750 A287751 A287752
350 A287753 A287754 A287755 A287756
353 A287757 A287758 A287759 A287760
355 A287778 A287779 A287780 A287781
358 A287782 A287783 A287784 A287785
361 A287786 A287787 A287788 A287789
363 A287848 A287849 A287850 A287851
366 A287852 A287853 A287854 A287855
369 A287856 A287857 A287858 A287859
371 A287902 A287903 A287904 A287905
374 A287906 A287907 A287908 A287909
377 A287910 A287911 A287912 A287913
379 A287941 A287942 A287946 A287947
382 A287948 A287949 A287950 A287951
387 A287952 A287953 A287954 A287955
389 A287975 A287976 A287977 A287978
390 A287979 A287980 A287981 A287982
395 A287983 A287984 A287985 A287986
397 A288008 A288009 A288010 A288011
398 A288012 A288013 A288014 A288015
403 A288016 A288017 A288018 A288019
406 A288042 A288043 A288044 A288045
411 A288046 A288047 A288048 A288049
414 A288050 A288051 A288052 A288053
417 A288056 A288057 A288058 A288059
419 A288060 A288061 A288062 A288063
421 A288064 A288065 A288066 A288067
422 A288121 A288123 A288124 A288125
425 A288127 A288128 A288129 A288130
427 A288131 A288136 A288137 A288138
429 A288190 A288191 A288192 A288193
430 A288194 A288195 A288196 A288197
433 A288198 A288200 A288201 A288202
435 A288292 A288293 A288294 A288295
437 A288296 A288297 A288298 A288299
438 A288300 A288301 A288302 A288303
441 A288328 A288329 A288330 A288331
443 A288332 A288333 A288334 A288335
446 A288336 A288337 A288338 A288339
449 A288357 A288358 A288359 A288360
451 A288361 A288362 A288363 A288364
453 A288365 A288366 A288367 A288368
454 A288393 A288394 A288395 A288396
457 A288397 A288398 A288399 A288400
459 A288401 A288402 A288403 A288404
461 A288431 A288432 A288433 A288434
462 A288435 A288436 A288437 A288438
467 A288439 A288440 A288441 A288442
470 A288494 A288495 A288496 A288497
475 A288498 A288499 A288500 A288501
478 A288503 A288504 A288505 A288506
481 A288584 A288585 A288586 A288587
483 A288588 A288589 A288590 A288591
485 A288592 A288593 A288594 A288595
486 A288642 A288643 A288644 A288645
489 A288646 A288647 A288648 A288649
491 A288650 A288651 A288652 A288653
493 A288661 A288662 A288663 A288664
494 A288697 A288698 A288699 A288700
497 A288701 A288702 A288704 A288705
499 A276540 A284040 A284041 A284042
501 A288020 A288761 A288762 A288763
502 A288764 A288765 A288766 A288767
505 A288768 A288769 A288770 A288771
507 A288801 A288802 A288803 A288804
510 A288805 A288806 A288807 A288808

2D 5-Neighbor Outer Totalistic Cellular Automata Sequences in the OEIS (concluded)
Rule In(B) Out(B) In(D) Out(D)
513,769
515,523
517
519,527,535,543,547,551,555,559,563,567,571,575,583,591,599,

607,611,615,619,623,627,631,635,639,647,655,663,671,675,679, 683,687,691,695,699,703,711,719,727,735,739,743,747,751,755, 759,763,767,775,783,791,799,803,807,811,815,819,823,827,831, 839,847,855,863,867,871,875,879,883,887,891,895,903,911,919, 927,931,935,939,943,947,951,955,959,967,975,983,991,995,999, 1003,1007,1011,1015,1019,1023

521
525
529
531
533
534
537
539
541
542
545
549
553
557
561
565
566,574,630,638,694,702,758,766,822,830,886,894,950,958,1014,

1022

569
573
577
579
581
585
587
589
593
595
597
598
601
603
605
606
609
613
617
621
625
629
633
637
641,649,897,905
643,651,707,715
645,653,661,669,677,685,693,701,709,717,725,733,741,749,757,

765

657,665
659,667,723,731
662
670
673,681,689,697
705,713
721,729
726
734
737,745,753,761,901,909,917,925,933,941,949,957,965,973,981,

989,993,997,1001,1005,1009,1013,1017,1021

771,787,835,851
773,781,789,797,837,845,853,861
774
777
779,795,843,859
782
785,793
790,854
798,862
801
805,821,869,885
806
809
813,829,877,893
814,942
817
825
833,849
838
841,857
846
865,881
870
873,889
878
899,907,915,923,963,971,979,987
902
910
913,921
918,982
926,990
929,937,945,953
934
961,977
966
969,985
974
998
1006

## Mathematica Program To Generate the Sequences Above

```(* Mathematica Program to Generate Outer Totalistic Cellular Automata Sequences *)
CAStep[rule_, a_] := Map[rule[ [10 - #] ] &, ListConvolve[{{0,2,0}, {2,1,2}, {0,2,0}}, a, 2], {2}];
code = 622; stages = 16;
rule = IntegerDigits[code, 2, 10];
(* Generate CA for this rule *)
g = 2*stages + 1;
a = PadLeft[{ {1} }, {g, g}, 0, Floor[{g, g}/2]];
ca = a;
ca = Table[ca = CAStep[rule, ca], {n, 1, stages + 1}];
PrependTo[ca, a];
(* Trim full grid to reflect growth by one cell at each stage *)
k = (Length[ca[ [1] ]] + 1)/2;
ca = Table[Table[Part[ca[ [n] ] [ [j] ], Range[k+1-n, k-1+n]], {j, k+1-n, k-1+n}], {n,1,k}];

"CA Evolution Diagrams"
lca = Length[ca];
For[is = 1, is ≤ lca, is++,
Print["\nStage ", is - 1];
c = ca[ [is] ];
lc = Length[c];
For[i = 1, i ≤ lc, i++,
line = c[ [i] ];
out = "";
For[j = 1, j ≤ lc, j++, out = out <> If[line[ [j] ] == 0, " .", " x"]];
Print[out];
]
];

"Counts of ON Cells at Each Stage"
on = Map[Function[Apply[Plus, Flatten[#1]]], ca]

"Counts of ON Cells at Stages 2^n-1"
Part[on, 2^Range[0, Log[2, stages]]]

"Partial Sums"
Table[Total[Part[on, Range[1, i]]], {i, 1, Length[on]}]

"First Differences"
Table[on[ [i + 1] ] - on[ [i] ], {i, 1, Length[on] - 1}]
```

## Output from the Mathematica Program To Generate the Sequences Above

```CA Evolution Diagrams

Stage  0
x

Stage  1
. x .
x x x
. x .

Stage  2
. . x . .
. . x . .
x x x x x
. . x . .
. . x . .

Stage  3
. . . x . . .
. . x x x . .
. x . x . x .
x x x x x x x
. x . x . x .
. . x x x . .
. . . x . . .

Stage  4
. . . . x . . . .
. . . . x . . . .
. . . x x x . . .
. . x . x . x . .
x x x x x x x x x
. . x . x . x . .
. . . x x x . . .
. . . . x . . . .
. . . . x . . . .

...

Stage  16
. . . . . . . . . . . . . . . . x . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . x . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . x x x . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . x x x x x . . . . . . . . . . . . . .
. . . . . . . . . . . . . x x . x . x x . . . . . . . . . . . . .
. . . . . . . . . . . . x x x . x . x x x . . . . . . . . . . . .
. . . . . . . . . . . x x x x x x x x x x x . . . . . . . . . . .
. . . . . . . . . . x x x . x x x x x . x x x . . . . . . . . . .
. . . . . . . . . x x x x . x x x x x . x x x x . . . . . . . . .
. . . . . . . . x . . x . x . x x x . x . x . . x . . . . . . . .
. . . . . . . x x . . . x . . x x x . . x . . . x x . . . . . . .
. . . . . . x x x x . . x x x x x x x x x . . x x x x . . . . . .
. . . . . x x x x . x x . x . . x . . x . x x . x x x x . . . . .
. . . . x x x . . x . x x . x x x x x . x x . x . . x x x . . . .
. . . x x x x x x . . x . x . x x x . x . x . . x x x x x x . . .
. . x x . . x x x x x x . x x . x . x x . x x x x x x . . x x . .
x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x
. . x x . . x x x x x x . x x . x . x x . x x x x x x . . x x . .
. . . x x x x x x . . x . x . x x x . x . x . . x x x x x x . . .
. . . . x x x . . x . x x . x x x x x . x x . x . . x x x . . . .
. . . . . x x x x . x x . x . . x . . x . x x . x x x x . . . . .
. . . . . . x x x x . . x x x x x x x x x . . x x x x . . . . . .
. . . . . . . x x . . . x . . x x x . . x . . . x x . . . . . . .
. . . . . . . . x . . x . x . x x x . x . x . . x . . . . . . . .
. . . . . . . . . x x x x . x x x x x . x x x x . . . . . . . . .
. . . . . . . . . . x x x . x x x x x . x x x . . . . . . . . . .
. . . . . . . . . . . x x x x x x x x x x x . . . . . . . . . . .
. . . . . . . . . . . . x x x . x . x x x . . . . . . . . . . . .
. . . . . . . . . . . . . x x . x . x x . . . . . . . . . . . . .
. . . . . . . . . . . . . . x x x x x . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . x x x . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . x . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . x . . . . . . . . . . . . . . . .

Counts of ON Cells at Each Stage
{1,5,9,21,25,37,57,69,89,101,121,133,169,205,257,309,361}

Counts of ON Cells at Stages 2^n-1
{1,5,21,69,309}

Partial Sums
{1,6,15,36,61,98,155,224,313,414,535,668,837,1042,1299,1608,1969}

First Differences
{4,4,12,4,12,20,12,20,12,20,12,36,36,52,52,52}
```

## Rules that generate equivalent counts of ON cells at stage 2^n-1

Rules in each of the lists below generate equivalent counts of ON cells at stage 2^n-1 based on the first 6 terms:

{0, 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112, 120, 128, 136, 144, 152, 160, 168, 176, 184, 192, 200, 208, 216, 224, 232, 240, 248, 256, 264, 272, 280, 288, 296, 304, 312, 320, 328, 336, 344, 352, 360, 368, 376, 384, 392, 400, 408, 416, 424, 432, 440, 448, 456, 464, 472, 480, 488, 496, 504, 512, 520, 528, 536, 544, 552, 560, 568, 576, 584, 592, 600, 608, 616, 624, 632, 640, 648, 656, 664, 672, 680, 688, 696, 704, 712, 720, 728, 736, 744, 752, 760, 768, 776, 784, 792, 800, 808, 816, 824, 832, 840, 848, 856, 864, 872, 880, 888, 896, 904, 912, 920, 928, 936, 944, 952, 960, 968, 976, 984, 992, 1000, 1008, 1016}

{1, 9, 17, 25, 257, 265, 273, 281, 673, 681, 689, 697}

{2, 10, 18, 26, 34, 42, 50, 58, 66, 74, 82, 90, 98, 106, 114, 122, 130, 138, 146, 154, 162, 170, 178, 186, 194, 202, 210, 218, 226, 234, 242, 250, 258, 266, 274, 282, 290, 298, 306, 314, 322, 330, 338, 346, 354, 362, 370, 378, 386, 394, 402, 410, 418, 426, 434, 442, 450, 458, 466, 474, 482, 490, 498, 506, 514, 522, 530, 538, 546, 554, 562, 570, 578, 586, 594, 602, 610, 618, 626, 634, 642, 650, 658, 666, 674, 682, 690, 698, 706, 714, 722, 730, 738, 746, 754, 762, 770, 778, 786, 794, 802, 810, 818, 826, 834, 842, 850, 858, 866, 874, 882, 890, 898, 906, 914, 922, 930, 938, 946, 954, 962, 970, 978, 986, 994, 1002, 1010, 1018}

{3, 11, 19, 27, 67, 75, 83, 91, 675, 683, 691, 699, 739, 747, 755, 763, 899, 907, 915, 923, 963, 971, 979, 987}

{4, 12, 36, 44, 68, 76, 84, 92, 100, 108, 116, 124, 132, 140, 164, 172, 196, 204, 212, 220, 228, 236, 244, 252, 276, 284, 308, 316, 340, 348, 372, 380, 404, 412, 436, 444, 468, 476, 500, 508, 516, 524, 548, 556, 580, 588, 596, 604, 612, 620, 628, 636, 644, 652, 676, 684, 708, 716, 724, 732, 740, 748, 756, 764, 788, 796, 820, 828, 852, 860, 884, 892, 916, 924, 948, 956, 980, 988, 1012, 1020}

{5, 13, 21, 29, 37, 45, 53, 61, 69, 77, 85, 93, 101, 109, 117, 125, 901, 909, 917, 925, 933, 941, 949, 957, 965, 973, 981, 989, 997, 1005, 1013, 1021}

{6, 38, 70, 102, 134, 166, 198, 230}

{7, 15, 23, 31, 39, 47, 55, 63, 71, 79, 87, 95, 103, 111, 119, 127, 135, 143, 151, 159, 167, 175, 183, 191, 199, 207, 215, 223, 231, 239, 247, 255, 263, 271, 279, 287, 295, 303, 311, 319, 327, 335, 343, 351, 359, 367, 375, 383, 391, 399, 407, 415, 423, 431, 439, 447, 455, 463, 471, 479, 487, 495, 503, 511, 519, 527, 535, 543, 551, 559, 567, 575, 583, 591, 599, 607, 615, 623, 631, 639, 647, 655, 663, 671, 679, 687, 695, 703, 711, 719, 727, 735, 743, 751, 759, 767, 775, 783, 791, 799, 807, 815, 823, 831, 839, 847, 855, 863, 871, 879, 887, 895, 903, 911, 919, 927, 935, 943, 951, 959, 967, 975, 983, 991, 999, 1007, 1015, 1023}

{14, 46, 142, 174}

{20, 28, 52, 60, 148, 156, 180, 188, 532, 540, 564, 572, 660, 668, 692, 700}

{35, 43, 59}

{65, 321}

{86, 342}

{129, 385, 425, 465, 553}

{131, 163, 171, 227, 235, 771, 787, 803, 811, 819, 827, 835, 851, 867, 875, 883, 891}

{145, 153}

{190, 254}

{221, 253}

{245, 501}

{260, 268, 292, 300, 388, 396, 420, 428, 772, 780, 804, 812, 900, 908, 932, 940}

{261, 269, 277, 285, 293, 301, 309, 317, 325, 333, 341, 349, 357, 365, 373, 381, 413, 445, 477, 509, 645, 653, 661, 669, 677, 685, 693, 701, 709, 717, 725, 733, 741, 749, 757, 765}

{324, 332, 356, 364, 452, 460, 484, 492, 836, 844, 868, 876, 964, 972, 996, 1004}

{337, 505}

{401, 409}

{430, 558, 598, 686, 750, 926, 990}

{510, 574, 638, 702, 766, 790, 830, 854, 894, 958, 1022}

{513, 769}

{515, 523}

{518, 550, 582, 614

{555, 571}

{619, 635}

{641, 649, 897, 905}

{643, 651, 707, 715}

{657, 665}

{659, 667, 723, 731, 931, 939, 947, 955, 995, 1003, 1011, 1019}

{705, 713}

{721, 729}

{737, 745, 753, 761, 993, 1001, 1009, 1017}

{773, 781, 789, 797, 837, 845, 853, 861}

{779, 795, 843, 859}

{798, 862}

{805, 821, 869, 885}

{813, 829, 877, 893}

{822, 886}

{833, 849}

{841, 857}

{865, 881}

{873, 889}

{913, 921, 929, 937, 945, 953}

{918, 982}

{950, 1014}

{961, 977}

{969, 985}