A245226 - OEIS

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

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OFFSET

1,2

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

LINKS

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

EXAMPLE

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

MATHEMATICA

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

PROG

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

CROSSREFS

Cf. A001481, A248151.

Sequence in context: A382092 A001481 A248151 * A034026 A125022 A378294

Adjacent sequences: A245223 A245224 A245225 * A245227 A245228 A245229

KEYWORD

nonn

AUTHOR

Colin Barker, Jul 14 2014

STATUS

approved