A257410 Values of n such that there are exactly 3 solutions to x^2 - y^2 = n with x > y >= 0.

45, 48, 63, 64, 72, 75, 80, 81, 99, 112, 117, 128, 147, 153, 171, 175, 176, 180, 200, 207, 208, 243, 245, 252, 261, 272, 275, 279, 300, 304, 324, 325, 333, 363, 368, 369, 387, 392, 396, 423, 425, 464, 468, 475, 477, 496, 507, 531, 539, 549, 575, 588, 592

Offset: 1

Author

Colin Barker, Apr 22 2015

Keywords

• nonn

Examples

			45 is in the sequence because there are 3 solutions to x^2 - y^2 = 45, namely (x,y) = (7,2),(9,6),(23,22).
		

Links

• Colin Barker, Table of n, a(n) for n = 1..500

Crossrefs

Cf. A257408, A257409, A257411-A257417.

Cf. A034178.

Programs

Mathematica

r[n_] := Reduce[x^2 - y^2 == n && x > y >= 0, {x, y}, Integers]; Reap[For[n = 1, n < 600, n++, rn = r[n]; If[rn[[0]] === Or && Length[rn] == 3, Print[n]; Sow[n]]]][[2, 1]] (* Jean-François Alcover, Apr 22 2015 *)

PARI

is_A257410(n)={A034178(n)==3} \\ M. F. Hasler, Apr 22 2015