A245226 Values of n such that the equation x^2 - n*y^2 = n has integer solutions.

1, 2, 4, 5, 8, 9, 10, 13, 16, 17, 18, 20, 25, 26, 29, 32, 36, 37, 40, 41, 45, 49, 50, 52, 53, 58, 61, 64, 65, 68, 72, 73, 74, 80, 81, 82, 85, 89, 90, 97, 98, 100, 101, 104, 106, 109, 113, 116, 117, 121, 122, 125, 128, 130, 137, 144, 145, 148, 149, 153, 157

Offset: 1

Author

Colin Barker, Jul 14 2014

Keywords

• nonn

Comments

All the squares are in this sequence.

Differs from A001481 \ {0} and A248151 from a(17) = 36 on. The number 0 is in the sequence according to its definition. - M. F. Hasler, Oct 22 2019

Examples

			5 is in the sequence because x^2-5*y^2=5 has integer solutions, including (x,y) = (5,2) and (85,38).
		

Links

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

Crossrefs

Cf. A001481, A248151.

Programs

Mathematica

Select[Range[1,200],Solve[x^2==#*(1+y^2),{x,y},Integers]!={}&] (* Vaclav Kotesovec, Jul 15 2014 *)

PARI

isok(m) = if (issquare(4*m), 1, #qfbsolve(Qfb(1, 0, -m), m, 2)); \\ Michel Marcus, May 17 2025