A277516 a(n) = smallest k >= 0 for which there is a sequence n = b_1 < b_2 < ... < b_t = n + k such that b_1 + b_2 +...+ b_t is a perfect square.

0, 0, 2, 3, 0, 5, 4, 2, 6, 0, 4, 2, 1, 5, 4, 3, 0, 2, 4, 4, 3, 6, 5, 3, 1, 0, 2, 6, 4, 6, 4, 2, 3, 5, 4, 5, 0, 5, 4, 3, 1, 7, 6, 4, 7, 5, 4, 2, 4, 0, 7, 6, 7, 6, 4, 3, 7, 6, 5, 3, 1, 5, 4, 4, 0, 8, 7, 8, 7, 6, 4, 2, 5, 4, 2, 8, 7, 6, 4, 4, 9, 0, 5, 3, 1, 6, 5

Offset: 0

Author

Peter Kagey, Oct 19 2016

Keywords

• nonn
• easy

Comments

Records occur at n = 1, 2, 3, 5, 8, 41, 65, 80, 90, 183, 292, 467, 627, 1428, 1547, 1666, 1999, 3568, 4012, 5737, 7458, 12119, 13640, 14365, 21859, 28445, 37408, 38839, 40763, 50346, 50347, 92063, ...

Examples

			a(1) = 0  via 1                 = 1^2;
a(2) = 2  via 2 + (2+1) + (2+2) = 3^2;
a(6) = 4  via 6 + (6+4)         = 4^2.
		

Links

• David A. Corneth, Table of n, a(n) for n = 0..9999 (First 3001 terms from Peter Kagey)

Crossrefs

Cf. A277278.

Programs

Haskell

a277516 n = a277278 n - n

Formula

a(n) = A277278(n) - n.