The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A277214 a(n) is the Manhattan distance between n and 1 in a 3-dimensional cubic spiral of positive integers with 1..8 at the center (illustration in the comments). 0
 0, 1, 2, 1, 2, 3, 2, 1, 2, 3, 4, 3, 4, 3, 4, 3, 4, 5, 4, 5, 6, 5, 4, 5, 4, 3, 2, 3, 2, 3, 4, 3, 4, 5, 4, 3, 2, 3, 4, 3, 2, 3, 2, 1, 2, 1, 2, 3, 4, 3, 4, 5, 4, 3, 4, 3, 2, 3, 2, 3, 2, 3, 2, 1, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Similar to A214526, but three-dimensional, and the core is 2 X 2 X 2 rather than 1 X 1. The spiral begins as follows: Level z=-2:    95  94  93  92  91  90    96  77  76  75  74  89    97  78  67  66  73  88    98  79  68  65  72  87    99  80  69  70  71  86   100  81  82  83  84  85 z=-1:   116 115 114 113 112 111   117  52  51  50  49 110   118  53  62  61  60 109   119  54  63  64  59 108   120  55  56  57  58 107   101 102 103 104 105 106 z=0:   137 136 135 134 133 132   138  39  38  37  48 131   139  40   3   2  47 130   140  41   4   1  46 129   121  42  43  44  45 128   122 123 124 125 126 127 z=1:   144 145 146 147 148 149   143  34  35  36  25 150   142  33   6   7  26 151   141  32   5   8  27 152   160  31  30  29  28 153   159 158 157 156 155 154 z=2:   165 166 167 168 169 170   164  21  22  23  24 171   163  20  11  12  13 172   162  19  10   9  14 173   161  18  17  16  15 174   180 179 178 177 176 175 z=3:   186 187 188 189 190 191   185 204 205 206 207 192   184 203 214 215 208 193   183 202 213 216 209 194   182 201 212 211 210 195   181 200 199 198 197 196 Algorithm sketch: 1. At every x-y plane the direction is clockwise if z > 0 and counterclockwise if z <= 0. 2. After an N*N cube is complete and we start building an M*M cube, M=N+2: 2a. The spiral at the first new edge of the M*M cube progresses from center to edges, in the same way as the A214526 spiral, e.g., z=-2 in the illustration. 2b. Between the first and last z-edges the spiral progresses according to item 1. 2c. The spiral at the last new edge of the M*M cube progresses from edges to center, e.g., z=3 in the illustration. LINKS FORMULA abs( a(n) - a(n-1) ) = 1. CROSSREFS Cf. A214526. Sequence in context: A043554 A005811 A008342 * A278603 A248218 A182110 Adjacent sequences:  A277211 A277212 A277213 * A277215 A277216 A277217 KEYWORD nonn AUTHOR Alex Ratushnyak, Oct 05 2016 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified June 21 04:10 EDT 2021. Contains 345354 sequences. (Running on oeis4.)