A082658 Integers expressible as the sum of a square and a triangular number in exactly two distinct ways.

7, 15, 22, 26, 28, 31, 40, 45, 52, 55, 59, 61, 67, 79, 85, 87, 92, 94, 100, 102, 103, 106, 114, 115, 124, 130, 140, 142, 147, 155, 157, 159, 166, 175, 178, 180, 184, 187, 189, 190, 191, 197, 202, 205, 206, 210, 211, 214, 220, 224, 231, 232, 240, 241, 246, 247

Offset

1,1

Comments

It is assumed here that 0 is a square but not a triangular number. - Amiram Eldar, Dec 08 2019

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

a(4) = 26 because 26 = 1 + 25; 26 = 10 + 16.

Mathematica

aQ[n_] := Length @ Solve[x^2 + y (y + 1)/2 == n && x >= 0 && y > 0, {x, y}, Integers] == 2; Select[Range[250], aQ] (* Amiram Eldar, Dec 08 2019 *)

Crossrefs

Cf. A000217, A000290, A082657, A082659, A082660.

Sequence in context: A346197 A274700 A022552 * A022389 A041225 A128840

Adjacent sequences: A082655 A082656 A082657 * A082659 A082660 A082661

Keyword

nonn

Author

Jason Earls, May 17 2003

Extensions

Name clarified by Amiram Eldar, Dec 08 2019

Status

approved