A050269 - OEIS

%I #15 Feb 04 2019 12:18:19

%S 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,

%T 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,

%U 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

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

%H P. Gibbs, <a href="https://arxiv.org/abs/math/0107203">Diophantine quadruples and Cayley's hyperdeterminant</a>, arXiv:math/0107203 [math.NT], 2001.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DiophantusProperty.html">Diophantus Property.</a>

%t 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 *)

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

%Y Cf. A050270.

%K nonn

%O 1,2

%A _Eric W. Weisstein_