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
Keywords
Examples
43 appears in the sequence because the equation x^2 - 43*y^2 = 86 has integer solutions, such as (x,y) = (387,59).
Programs
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Mathematica
Select[Range[200],FindInstance[x^2-#*y^2==2*#,{x,y},Integers]!={}&] (* Harvey P. Dale, Jun 22 2019 *) -
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