A049239 - OEIS

%I #8 Oct 10 2016 02:45:02

%S 0,1,1,1,0,2,0,2,1,0,1,2,0,2,1,1,2,3,1,2,2,1,2,3,0,2,4,3,1,1,3,4,1,3,

%T 5,4,0,0,3,4,0,2,1,0,0,1,2,3,1,5,1,3,5,1,1,1,2,3,4,5,0,2,4,6,2,2,1,2,

%U 2,0,5,6,1,3,0,7,1,3,1,2,1,4,5,6,0,2,1,4,8,4,1,1,2,0,1,5,6,7,1,3,5,7,0,2,5

%N Smallest nonnegative value taken on by px^2-qy^2 for an infinite number of integer pairs (x,y), where (p,q) = (1,1), (1,2), (2,1), (1,3), (2,2), (3,1)...

%e Array begins:

%e 0,  1,  1,  0,  1, ...

%e 1,  0,  2,  2,  2, ...

%e 2,  1,  0,  3,  3, ...

%e 0,  2,  1,  0,  4, ...

%e 1,  2,  2,  1,  0, ...

%e ...

%t f[p_, q_, z_] := FindInstance[x > 0 && y > 0 && p*x^2 - q*y^2 == z, {x, y}, Integers, 1]; a[p_, q_] := For[z = 0, True, z = z + GCD[p, q], fz = f[p, q, z]; If[fz =!= {}, Print["a(", p, " ", q, ") = ", z, " {x,y} = ", {x, y} /. fz[[1]]]; Return[z]]]; Table[TimeConstrained[a[p - q + 1, q], 300], {p, 1, 14}, {q, p, 1, -1}] // Flatten (* _Jean-François Alcover_, Oct 10 2016 *)

%K nonn,tabl

%O 1,6

%A _David W. Wilson_