A188898 The index of the least n-gonal number greater than 1 that is also square, or 0 if none exists.

8, 2, 81, 25, 6, 9, 2, 0, 7, 4, 3, 9, 22, 2, 49, 4, 8, 0, 17, 9, 81, 5, 2, 25, 46, 3, 10, 121, 6, 9, 18, 4, 31, 2, 11, 169, 7, 6, 1681, 49, 8, 4, 4961, 12, 225, 8, 2, 16, 32, 0, 49, 25, 17, 13, 289, 9, 49, 7, 27, 81, 118, 2, 136161, 196, 14, 4, 10, 841, 1521

Offset: 3

Author

T. D. Noe, Apr 13 2011

Keywords

• nonn

Comments

Sequence A188896 gives the n that have no solution.

Crossrefs

Cf. A100252 (least square n-gonal number greater than 1).

Programs

Mathematica

kMax = 25000; NgonIndex[n_, v_] := (-4 + n + Sqrt[16 - 8*n + n^2 - 16*v + 8*n*v])/(n - 2)/2; Table[k = 2; While[sqr = k^2; i = NgonIndex[n, sqr]; k < kMax && ! IntegerQ[i], k++]; If[k == kMax, k = sqr = i = 0]; i, {n, 3, 64}]

Formula

If n is a square, then a(n)=2.