|
%I #14 Apr 03 2023 10:36:12
%S 0,1819380158564160,117124856755987405647781716823680,
%T 7540058082713667504003446125203741470945194284480,
%U 485400601250164750241979240919394389707542655611270208094258863360
%N y-values in the solutions to x^2 - 313*y^2 = 1.
%D A. H. Beiler, Recreations in the Theory of Numbers, Dover, NY, 1996, p. 248.
%H G. L. Honaker, Jr. and Chris Caldwell, <a href="https://t5k.org/curios/cpage/40.html">Prime Curios! 313</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (64376241658269698, -1).
%F a(n) = 64376241658269698*a(n-1) - a(n-2) with a(1) = 0 and a(2) = 1819380158564160.
%F G.f.: 1819380158564160*x^2/(1 - 64376241658269698*x + x^2).
%t LinearRecurrence[{64376241658269698, -1}, {0, 1819380158564160}, 5]
%o (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
%Y Cf. A041591, A082393.
%K nonn,easy
%O 1,2
%A _Arkadiusz Wesolowski_, Jan 15 2012
| 