1,1

If A=[A157724] 15625*n.^2-29114*n+13562 (73, 17834, 66845, ,..,); Y=[A157725] 3906250*n-3639250 (267000, 4173250, 8079500,..,); X=[A157726] 488281250*n^2-909812500*n + 423812499 (2281249, 557312499,..,), we have, for all terms, Pell's equation X^2-A*Y^2=1. Example: 2281249^2-73*267000^2=1; 557312499^2-17834*4173250^2=1.

Vincenzo Librandi, X^2-AY^2=1

Edward Everett Withford, Pell Equation

Wolfram MathWorld, Pell Equation

a(n)=488281250*n^2-909812500*n+423812499 (n>0)

For n=1, a(1)=2281249; n=2, a(2)=557312499; n=3, a(3)=2088906249

Cf. A157724, A157725

Sequence in context: A046444 A089445 A089446 this_sequence A092017 A154676 A167438

Adjacent sequences: A157723 A157724 A157725 this_sequence A157727 A157728 A157729

nonn

Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 05 2009