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

0,3

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, ...

Links

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

Formula

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

Example

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.

Prog

(Haskell)
a277516 n = a277278 n - n

Crossrefs

Cf. A277278.

Sequence in context: A354365 A066913 A090303 * A322333 A346615 A240667

Adjacent sequences: A277513 A277514 A277515 * A277517 A277518 A277519

Keyword

nonn,easy

Author

Peter Kagey, Oct 19 2016

Status

approved