A101158 Let j be the smallest integer for which n+(n+1)+...+(n+j) is a square; sequence gives the squares.

1, 9, 25, 4, 81, 121, 169, 225, 9, 361, 36, 25, 625, 729, 841, 16, 1089, 100, 1369, 1521, 196, 1849, 2025, 49, 25, 81, 2809, 3025, 3249, 3481, 3721, 324, 4225, 4489, 225, 36, 324, 5625, 484, 81, 6561, 6889, 225, 7569, 441, 676, 144, 9025, 49, 9801

Offset: 1

Author

Charlie Marion, Dec 29 2004

Keywords

• nonn

Comments

Basis for sequence is shortest arithmetic sequence with initial term n and difference 1 that sums to a perfect square. Cf. A100251, A100252, A100253, A100254.

Examples

			a(11)=36 since 11+12+13 = 36.
		

Links

• Shawn A. Broyles, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A101157, A101159, A101160.

Formula

n+(n+1)+...+(n+A101160(n)) = n+(n+1)+...+A101159(n) = A101157(n)^2 = a(n).

a(n^2) = n^2. - Michel Marcus, Jun 28 2013

Extensions

a(21) corrected by Michel Marcus, Jun 29 2013