1,1

Arises in solving Pell equations of the form X^2 - A*Y^2 = 1.

Let n=[A156849] (156,373,685,902,...,) =n^2-2=0 mod (23^2). If A=[A156841] (46,263,1538,3871,.,) = 529*n^2-312*n+46 or A=[156842] (263,46,887,2787) =(529*n^2-746*n+263 , Y=23*n, or [A156845] (3588,15755,27922,...,) = 12167*n-8579, or Y=[A156846] (8579,20746,32913,...,) =12167*n-3588, and X=279841*n^2-165048*n+24335 [A156843] (24335,139128,813603,...,) or X=[A156844] =279841*n^2-394634*n+139128 (139128,24335,469224,1473795,...,) , we have for all terms, Pell's equation X^2-A*Y^2=1. Example: For n=156, A=46, Y=3588, X=24335, 24335^2-46*3588^2=1 ; n=373, A=263, Y=8579, X=139128; 139128^2-263*8579^2=1; n=685, A=887, Y=15755, X=469224; 469224^2-887*15755^2=1; n=902, A=1538, Y=20746, X=813603; 813603^2-1538*20746^2=1. [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Feb 20 2009]

Vincenzo Librandi, X^2-AY^2=1 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Feb 20 2009]

For n=0, a(0)=24335; n=1, a(1)=139128; n=2,a(2)=813603

Cf. A156844

Cf. A156841, A156842, A156845, A156846, A156849 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Feb 20 2009]

Sequence in context: A154069 A140923 A025041 this_sequence A083621 A083622 A052356

Adjacent sequences: A156840 A156841 A156842 this_sequence A156844 A156845 A156846

nonn

Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Feb 17 2009