A204419 y-values in the solutions to x^2 - 313*y^2 = 1.

0, 1819380158564160, 117124856755987405647781716823680, 7540058082713667504003446125203741470945194284480, 485400601250164750241979240919394389707542655611270208094258863360

Offset: 1

Author

Arkadiusz Wesolowski, Jan 15 2012

Keywords

• nonn
• easy

References

• A. H. Beiler, Recreations in the Theory of Numbers, Dover, NY, 1996, p. 248.

Links

• G. L. Honaker, Jr. and Chris Caldwell, Prime Curios! 313
• Index entries for linear recurrences with constant coefficients, signature (64376241658269698, -1).

Crossrefs

Cf. A041591, A082393.

Programs

Magma

I:=[0,1819380158564160]; [n le 2 select I[n] else 64376241658269698*Self(n-1)-Self(n-2): n in [1..10]]; // Vincenzo Librandi, May 16 2015

Mathematica

LinearRecurrence[{64376241658269698, -1}, {0, 1819380158564160}, 5]

Formula

a(n) = 64376241658269698*a(n-1) - a(n-2) with a(1) = 0 and a(2) = 1819380158564160.

G.f.: 1819380158564160*x^2/(1 - 64376241658269698*x + x^2).