A257409 Values of n such that there are exactly 2 solutions to x^2 - y^2 = n, with x > y >= 0.

9, 15, 16, 21, 24, 25, 27, 32, 33, 35, 36, 39, 40, 49, 51, 55, 56, 57, 60, 65, 69, 77, 84, 85, 87, 88, 91, 93, 95, 100, 104, 108, 111, 115, 119, 121, 123, 125, 129, 132, 133, 136, 140, 141, 143, 145, 152, 155, 156, 159, 161, 169, 177, 183, 184, 185, 187, 196

Offset: 1

Author

Colin Barker, Apr 22 2015

Keywords

• nonn

Comments

A subsequence of A058957. Terms in the latter but not here are 45, 48, 63, 64, 72, 75, 80, 81, 96, 99, ... - M. F. Hasler, Apr 22 2015

Examples

			9 is in the sequence because there are 2 solutions to x^2 - y^2 = 9, namely (x,y) = (3,0), (5,4).
		

Links

• Colin Barker, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A257408, A257410-A257417.

Cf. A058957, A034178.

Programs

Mathematica

r[n_] := Reduce[x^2 - y^2 == n && x > y >= 0, {x, y}, Integers]; Reap[For[n = 1, n < 200, n++, rn = r[n]; If[rn[[0]] === Or && Length[rn] == 2, Print[n]; Sow[n]]]][[2, 1]] (* Jean-François Alcover, Apr 22 2015 *)

PARI

is_A257409(n)={A034178(n)==2} \\ M. F. Hasler, Apr 22 2015