OFFSET
1,2
COMMENTS
The sequence A330979 gives the visited primes for a walk on the Ulam Spiral which starts at 1 and then steps to the square containing the closest unvisited prime number. This sequences lists the records for the square of the step distance between primes for that walk. For a walk of 10 million steps the largest square distance is 955620, approximately 977.6 units, which occurs between A330979(8165267) = 22147771, which has coordinates (-2353,1019) relative to the starting 1-square, to A330979(8165268) = 8236981 with coordinates (-1435,1355). See A330979 for an image of the walk. It is unknown if this is a finite or infinite sequence.
LINKS
Wikipedia, Ulam Spiral.
EXAMPLE
The below table shows the details of the record step lengths of this sequence. The coordinate is relative to the starting 1-square.
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a(n) | A330979 step # | Start prime & coord | End prime & coord |
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1 | 1 | 1 (0,0) | 2 (1,0) |
2 | 3 | 3 (1,1) | 11 (2,0) |
4 | 8 | 59 (2,4) | 61 (0,4) |
8 | 14 | 193 (-3,7) | 101 (-5,5) |
10 | 38 | 167 (4,-6) | 83 (5,-3) |
32 | 59 | 631 (13,7) | 1103 (17,3) |
74 | 169 | 113 (-3,-5) | 53 (4,0) |
90 | 319 | 17239 (66,12) | 22291 (75,15) |
136 | 1152 | 2719 (-26,12) | 4127 (-32,2) |
290 | 1659 | 13187 (19,-57) | 7907 (30,-44) |
360 | 2607 | 45263 (0,-106) | 40283 (-18,-100) |
388 | 7397 | 29723 (-86,-52) | 35509 (-94,-70) |
394 | 7806 | 47653 (-109,-19) | 59663 (-122,-4) |
674 | 7877 | 83101 (-144,-12) | 114419 (-169,-5) |
802 | 24920 | 2637497 (-812,692) | 2515477 (-793,713) |
872 | 27038 | 1285799 (-409,567) | 1170607 (-423,541) |
1184 | 55427 | 720089 (-288,-424) | 653761 (-316,-404) |
1394 | 56478 | 460349 (-339,-325) | 457687 (-304,-338) |
3316 | 56480 | 452293 (-300,-336) | 410203 (-320,-282) |
4100 | 82533 | 156353 (198,130) | 129263 (158,180) |
5300 | 83192 | 394211 (-140,314) | 331697 (-208,288) |
5634 | 165879 | 63589 (-126,42) | 161761 (-201,45) |
10728 | 237806 | 1034387 (509,-411) | 962543 (491,-309) |
23098 | 556765 | 110603 (-120,-166) | 19249 (-3,-69) |
25128 | 770967 | 7070333 (1330,-1278) | 8614337 (1468,-1356) |
26836 | 1074758 | 3213377 (-576,-896) | 3582083 (-420,-946) |
33508 | 1074809 | 4140079 (-129,-1017) | 2995469 (-27,-865) |
53954 | 2257389 | 67480409 (-1709,-4107) | 72669481 (-1882,-4262) |
61092 | 2644510 | 5269679 (790,1148) | 5492621 (544,1172) |
66610 | 2644988 | 1156873 (366,538) | 694591 (417,285) |
92858 | 2669627 | 109789 (166,62) | 122443 (-117,175) |
187540 | 2730402 | 2509621 (-792,228) | 672787 (-410,24) |
190120 | 2730411 | 193771 (-220,50) | 296827 (74,-272) |
215104 | 2730444 | 1505201 (285,-613) | 4506473 (405,-1061) |
217732 | 8160823 | 61908241 (-3934,1118) | 48110423 (-3468,1142) |
955620 | 8165267 | 22147771 (-2353,1019) | 8236981 (-1435,1355) |
CROSSREFS
KEYWORD
nonn,walk,more
AUTHOR
Scott R. Shannon, Jan 07 2020
EXTENSIONS
a(17)-a(20) from Scott R. Shannon, Jan 10 2020
a(7) and beyond corrected by Scott R. Shannon, Feb 02 2020
STATUS
approved