1,1

If A=[A157727] 15625*n.^2-2136*n+73 (13562, 58301, 134290, ,..,); Y=[A157728] 3906250*n- 267000 (3639250, 7545500,..,); X=[A157729] 488281250*n^2-66750000*n + 2281249 (423812499, 1821906249,..,), we have, for all terms, Pell's equation X^2-A*Y^2=1. Example: 423812499^2-13562*3639250^2=1; 1821906249^2-58301*7545500^2=1.

Edward Everett Withford, Pell Equation

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

Wolfram MathWorld, Pell Equation

a(n)=488281250*n^2-66750000*n+2281249 (n>0)

For n=1, a(1)=42381249; n=2, a(2)=1821906249; n=3, a(3)=4196562499

Cf. A157727, A157728

Sequence in context: A038132 A101770 A166024 this_sequence A017408 A017528 A117631

Adjacent sequences: A157726 A157727 A157728 this_sequence A157730 A157731 A157732

nonn

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