A365960 Sum of the 6 nearest neighbors of n in a hexagonal spiral with positive integers.

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

Author

Eric Angelini and Giorgos Kalogeropoulos, Sep 23 2023

Keywords

• nonn

Examples

			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.
		

Links

• Eric Angelini, An hexagonal seq?, Personal blog "Cinquante signes", Sept 2023.
• Eric Angelini, An hexagonal seq?, Personal blog "Cinquante signes", Sept 2023 [Cached copy]

Crossrefs

Cf. A214176, A278181, A278619.

Programs

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]]