A101160 a(n) is the smallest integer j for which n+(n+1)+...+(n+j) is a square.

0, 2, 4, 0, 8, 10, 12, 14, 0, 18, 2, 1, 24, 26, 28, 0, 32, 4, 36, 38, 7, 42, 44, 1, 0, 2, 52, 54, 56, 58, 60, 8, 64, 66, 5, 0, 7, 74, 10, 1, 80, 82, 4, 86, 8, 12, 2, 94, 0, 98, 100, 17, 14, 106, 108, 110, 7, 9, 116, 1, 120, 23, 124, 0, 128

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.

0 <= a(n) <= 2*(n - 1). - Ctibor O. Zizka, Oct 05 2023

Examples

			a(11)=2 since j=2 is the smallest integer for which 11+...+11+j = 6^2 = 36 is a perfect square.
		

Links

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

Crossrefs

Cf. A101157, A101158, A101159.

Cf. A100251, A100252, A100253, A100254.

Programs

PARI

a(n) = {j = 0; while(! issquare(sum(k=0, j, n+k)), j++); j;} \\ Michel Marcus, Sep 01 2013

Formula

n+(n+1)+...+(n+a(n)) = n+(n+1)+...+A101159(n) = A101157(n)^2 = A101158(n).

a(n^2) = 0. - Michel Marcus, Jun 28 2013

Extensions

More terms from Michel Marcus, Jun 28 2013