A230108 Values of d such that the equation x^2 - d*y^2 = 2*d has integer solutions.

2, 3, 6, 8, 11, 12, 18, 19, 22, 24, 27, 32, 38, 43, 44, 48, 50, 51, 54, 59, 66, 67, 72, 75, 76, 83, 86, 88, 96, 98, 99, 102, 107, 108, 114, 118, 123, 128, 131, 134, 139, 146, 147, 150, 152, 162, 163, 166, 171, 172, 176, 178, 179

Offset

1,1

Links

Table of n, a(n) for n=1..53.

Example

43 appears in the sequence because the equation x^2 - 43*y^2 = 86 has integer solutions, such as (x,y) = (387,59).

Mathematica

Select[Range[200], FindInstance[x^2-#*y^2==2*#, {x, y}, Integers]!={}&] (* Harvey P. Dale, Jun 22 2019 *)

Prog

(PARI) is(n)=sol=bnfisintnorm(bnfinit(z^2-n), 2*n); if(!#sol, 0, p=polcoeff(sol[1], 0); p==floor(p)) \\ Ralf Stephan, Oct 19 2013

Crossrefs

Cf. A172000, A230109.

Sequence in context: A020489 A002240 A099798 * A097383 A072893 A349662

Adjacent sequences: A230105 A230106 A230107 * A230109 A230110 A230111

Keyword

nonn

Author

Colin Barker, Oct 09 2013

Status

approved