A041591 -id:A041591 - cp's OEIS frontend

A041590 Numerators of continued fraction convergents to sqrt(313).

17, 18, 53, 230, 2583, 2813, 5396, 19001, 43398, 105797, 360789, 466586, 827375, 9567711, 39098219, 87764149, 126862368, 4401084661, 4527947029, 13456978719, 58355861905, 655371459674, 713727321579

Offset: 0

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 253724736, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1).

Cf. A041591.

Numerator[Convergents[Sqrt[313], 30]] (* Vincenzo Librandi, Nov 04 2013 *)

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

Original entry on oeis.org

0, 1819380158564160, 117124856755987405647781716823680, 7540058082713667504003446125203741470945194284480, 485400601250164750241979240919394389707542655611270208094258863360

Offset: 1

Arkadiusz Wesolowski, Jan 15 2012

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

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

Cf. A041591, A082393.

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

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

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).

cp's OEIS Frontend

A041590 Numerators of continued fraction convergents to sqrt(313).

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