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A365960
Sum of the 6 nearest neighbors of n in a hexagonal spiral with positive integers.
0
27, 38, 40, 48, 56, 64, 54, 78, 86, 72, 100, 84, 114, 96, 128, 108, 142, 120, 126, 162, 138, 176, 150, 156, 196, 168, 174, 216, 186, 192, 236, 204, 210, 256, 222, 228, 234, 282, 246, 252, 302, 264, 270, 276, 328, 288, 294, 300, 354, 312, 318, 324, 380, 336, 342, 348, 406, 360, 366, 372, 378, 438, 390, 396, 402
OFFSET
1,1
LINKS
Eric Angelini, An hexagonal seq?, Personal blog "Cinquante signes", Sept 2023.
EXAMPLE
Spiral begins:
49--48--47--46--45
/ \
50 28--27--26--25 44
/ / \ \
51 29 13--12--11 24 43
/ / / \ \ \
52 30 14 4---3 10 23 42
/ / / / \ \ \ \
53 31 15 5 1---2 9 22 41
\ \ \ \ / / /
54 32 16 6---7---8 21 40
\ \ \ / /
55 33 17--18--19--20 39
\ \ /
56 34--35--36--37--38
\
57--58--59--60--61
.
The 6 nearest neighbors of 2 are 1,3,7,8,9,10. Their sum is a(2)=38.
MATHEMATICA
step=9; ta[x_]:=Table[12, x]; f=Flatten[Table[Table[{ta[If[m==2, k-1, k]], 16+2m+12k}, {m, 6}], {k, 0, step}]][[3;; ]]; Join[{27, 38}, f+6Range[3, Length@f+2]]
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved