# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a049244 Showing 1-1 of 1 %I A049244 #9 Oct 10 2016 02:45:46 %S A049244 1,2,2,1,0,5,5,5,5,5,1,5,5,5,5,4,3,2,1,0,5,5,5,5,5,5,2,5,5,5,1,5,3,5, %T A049244 5,5,5,5,5,5,1,3,2,1,0,5,5,5,5,5,5,5,3,5,5,5,5,5,1,5,1,2,5,5,5,5,2,5, %U A049244 5,5,1,5,5,5,5,4,3,2,1,0,5,5,2,5,5,5,5,5,5,5,5,5,5,5,5,5,5,3,5,5,1,5,5,5,5 %N A049244 Smallest nonnegative value taken on by 5x^2 - ny^2 for an infinite number of integer pairs (x, y). %t A049244 f[n_, z_] := FindInstance[x > 0 && y > 0 && 5*x^2 - n*y^2 == z, {x, y}, Integers, 1]; a[n_] := For[z = 0, z <= 5, z = z + GCD[n, 5], fz = f[n, z]; If[fz =!= {}, Print["a(", n, ") = ", z, " {x,y} = ", {x, y} /. fz[[1]]]; Return[z]]]; %t A049244 a[49] := (Print["a(49) = ", 5, " {x,y} = ", {51841, 16560}]; 5); %t A049244 a[81] := (Print["a(81) = ", 5, " {x,y} = ", {161, 40}]; 5); %t A049244 a[83] := (Print["a(83) = ", 5, " {x,y} = ", {1919, 471}]; 5); %t A049244 a[98] := (Print["a(98) = ", 3, " {x,y} = ", {31, 7}]; 3); %t A049244 Table[TimeConstrained[a[n], 300], {n, 1, 105}] (* _Jean-François Alcover_, Oct 10 2016 *) %K A049244 nonn %O A049244 1,2 %A A049244 _David W. Wilson_ # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE