A360663 a(n) is the least integer m >= 3 such that n is a centered m-gonal number.

3, 4, 5, 6, 7, 8, 3, 10, 11, 4, 13, 14, 5, 16, 17, 3, 19, 20, 7, 22, 23, 4, 25, 26, 9, 28, 29, 3, 31, 32, 11, 34, 35, 6, 37, 38, 13, 4, 41, 7, 43, 44, 3, 46, 47, 8, 49, 5, 17, 52, 53, 9, 55, 56, 19, 58, 59, 4, 61, 62, 3, 64, 65, 11, 67, 68, 23, 7, 71, 12, 73, 74, 5, 76, 77, 13, 79

Offset

4,1

Links

Table of n, a(n) for n=4..80.

Eric Weisstein's World of Mathematics, Centered Polygonal Number.

Wikipedia, Centered polygonal number.

Example

a(16) = 5 since 16 is a centered pentagonal number, but not a centered square or centered triangular number.

Mathematica

seq[len_] := Module[{s = Table[0, {len}], c = 0, k = 3, n, ckn}, While[c < len, n = 2; While[(ckn = k*n*(n - 1)/2 - 2) <= len, If[s[[ckn]] == 0, c++; s[[ckn]] = k]; n++]; n = 4; k++]; s]; seq[100] (* Amiram Eldar, Mar 06 2023 *)

Crossrefs

Cf. A101321, A176774, A333914.

Sequence in context: A088243 A154660 A004492 * A333914 A140255 A050270

Adjacent sequences: A360660 A360661 A360662 * A360664 A360665 A360666

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 15 2023

Status

approved