A120744 Least k>0 such that a centered polygonal number nk(k+1)/2+1 is a perfect square; or -1 if no such number exists.

2, -1, 1, 3, 2, 7, 15, 1, 16, 8, 14, 4, 5, 15, 1, 2, 5, -1, 6, 3, 2, 39, 6, 1, 21, 7, 110, 3, 15, 7, 15, -1, 2, 8, 1, 4, 989, 8, 14, 2, 45, 15, 9, 4, 5, 335, 9, 1, 29, -1, 30, 15, 10, 415, 6, 2, 10, 32, 54, 3, 77, 55, 1, 5, 2, 7, 47750, 11, 15, 23, 47, -1, 48, 24, 16, 12, 5, 8, 2639, 1, 6720, 704, 38, 4, 2, 39, 505, 3, 13, 56, 9, 20, 13, 1631, 41

Offset: 1

Author

Alexander Adamchuk, Apr 26 2007

Keywords

• sign

Examples

			a(5) = 2 because A129556(2) = 2>1 and A129556(1) = 0<1.
		

Links

• Max Alekseyev, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Centered Polygonal Number

Crossrefs

Cf. A001542, A006451, A001921, A129444, A001570, A001652, A129556, A053606, A105038, A105040, A053141, A061278.

Formula

a(n) = -1 for n in A166259.

a(n) = 1 for n = k^2-1.

Extensions

Edited and b-file provided by Max Alekseyev, Jan 20 2010