A257408 Values of n such that there is exactly 1 solution to x^2 - y^2 = n with x > y >= 0.

1, 3, 4, 5, 7, 8, 11, 12, 13, 17, 19, 20, 23, 28, 29, 31, 37, 41, 43, 44, 47, 52, 53, 59, 61, 67, 68, 71, 73, 76, 79, 83, 89, 92, 97, 101, 103, 107, 109, 113, 116, 124, 127, 131, 137, 139, 148, 149, 151, 157, 163, 164, 167, 172, 173, 179, 181, 188, 191, 193

Offset: 1

Author

Colin Barker, Apr 22 2015

Keywords

• nonn

Comments

The terms a(1)=1 and a(3)=4 are the only squares in this sequence. - M. F. Hasler, Apr 22 2015

Examples

			13 is in the sequence because there is only 1 solution to x^2 - y^2 = 13, namely (x,y) = (7,6).
		

Links

• Colin Barker, Table of n, a(n) for n = 1..1500

Crossrefs

Cf. A257409-A257417.

Cf. A034178.

Programs

Mathematica

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

PARI

is(n)=A034178(n)==1 \\ M. F. Hasler, Apr 22 2015