A101157 Let j be the smallest integer for which n+(n+1)+...+(n+j) is a square, say k^2; then a(n)=k.

1, 3, 5, 2, 9, 11, 13, 15, 3, 19, 6, 5, 25, 27, 29, 4, 33, 10, 37, 39, 14, 43, 45, 7, 5, 9, 53, 55, 57, 59, 61, 18, 65, 67, 15, 6, 18, 75, 22, 9, 81, 83, 15, 87, 21, 26, 12, 95, 7, 99, 101, 33, 30, 107, 109, 111, 22, 25, 117, 11, 121, 42, 125, 8, 129

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.

a(n) is the least k>0 such that triangular(n-1) + k^2 is a triangular number. - Alex Ratushnyak, May 17 2013

Examples

			a(11)=6 since 11+12+13 = 6^2.
		

Links

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

Crossrefs

Cf. A101158, A101159, A101160.

Programs

PARI

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

Formula

n+(n+1)+...+(n+A101160(n)) = n+(n+1)+...+A101159(n) = a(n)^2 = A101158(n).

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

Extensions

More terms from Michel Marcus, Jun 28 2013