1,1

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

Let n=[A156718] (70,99,239,268,408,437,...,). If A=[A156640] (29,338,985,...,) or A=[156639] (29,58,425) =(n^2+1)/13^2 , Y=26*n, [A156636] (1820,6214,10608,...,) or Y=[A156627] (2574,6968,11362,...,) and X=2*n^2+1 [A156721] (9801,19603,143649,...,) or X=[A156735] (9801,114243,332929,...,) , we have for all terms, Pell's equation X^2-A*Y^2=1. Example: For n=70, A=29, Y=1820, X=9801; 9801^2-29*1820^2=1; n=99, A=58, Y=2574, X=19603; 19603^2-58*2574^2=1; n=239, A=338, Y=6214, X=114243; 114243^2-338*6214^2=1; n=268, A=425, Y=6968, X=143649; 143649^2-425*6968^2=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)=9801; n=1, a(1)=114243; n=2, a(2)=332929

Cf. A156721

Cf. A156718, A156639, A156640, A156636, A156627 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Feb 20 2009]

Sequence in context: A035911 A069333 A156721 this_sequence A113937 A036353 A031687

Adjacent sequences: A156732 A156733 A156734 this_sequence A156736 A156737 A156738

nonn

Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Feb 15 2009