A050269 Smallest value a for Diophantine 1-doubles (a,b) ordered by smallest b.

1, 2, 3, 4, 5, 1, 3, 6, 7, 8, 9, 2, 4, 10, 11, 12, 1, 8, 13, 3, 5, 14, 15, 16, 17, 4, 6, 18, 3, 8, 19, 20, 21, 1, 2, 5, 7, 12, 15, 22, 23, 24, 25, 6, 8, 26, 27, 4, 12, 28, 29, 7, 9, 30, 3, 16, 31, 32, 1, 24, 33, 8, 10, 34, 35, 36, 5, 16, 37, 2, 3, 9, 11, 21, 24, 38, 39, 4, 20, 40, 41

Offset: 1

Author

Eric W. Weisstein

Keywords

• nonn

Links

• P. Gibbs, Diophantine quadruples and Cayley's hyperdeterminant, arXiv:math/0107203 [math.NT], 2001.
• Eric Weisstein's World of Mathematics, Diophantus Property.

Crossrefs

Cf. A050270.

Programs

Mathematica

m = 0; Do[If[IntegerQ[Sqrt[a*b + 1]], an[m++] = a], {b, 2, 43}, {a, 1, b}]; Array[an, 81, 0] (* Jean-François Alcover, Feb 04 2019 *)

PARI

an=vector(81); m=0; for(b=2,43, for(a=1,b, if(issquare(a*b+1), an[ m++ ]=a))); an