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 A114046 Numbers x such that x^2 - 92*y^2 = 1. 1
 1, 1151, 2649601, 6099380351, 14040770918401, 32321848554778751, 74404881332329766401, 171280004505174567476351, 394286495966030522000793601, 907647342433797756471259393151, 2089403787996106469366317122240001, 4809806612319694658683505544137089151 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Quote from the link prompting this sequence. A person who can, within a year, solve x^2 - 92y^2 = 1 is a mathematician. Brahmagupta [598-668] This sequence is computed with g(1e9,92) in the pari program. A Pell equation - Benoit Cloitre, Feb 03 2006 LINKS Harvey P. Dale, Table of n, a(n) for n = 0..297 Author?, Title? Tanya Khovanova, Recursive Sequences John Robertson, Home page. Index entries for linear recurrences with constant coefficients, signature (2302, -1). FORMULA a(0)=1, a(1)=1151 then a(n)=2302*a(n-1)-a(n-2) - Benoit Cloitre, Feb 03 2006 G.f.: (1-1151x)/(1-2302x+x^2). [From Philippe Deléham, Nov 18 2008] a(n)=1/2*{[1151-240*sqrt(23)]^n+[1151+240*sqrt(23)]^n}, with n>=0 [From Paolo P. Lava, Nov 24 2008] EXAMPLE (1151^2 - 1)/92 = 120^2. MATHEMATICA LinearRecurrence[{2302, -1}, {1, 1151}, 12] (* Ray Chandler, Aug 11 2015 *) PROG (PARI) g(n, k) = for(y=0, n, x=k*y^2+1; if(issquare(x), print1(floor(sqrt(x))", "))) (PARI) a0=1; a1=1151; for(n=2, 30, a2=2302*a1-a0; a0=a1; a1=a2; print1(a2, ", ")) (Cloitre) CROSSREFS Sequence in context: A179037 A098976 A154374 * A035888 A252438 A179689 Adjacent sequences:  A114043 A114044 A114045 * A114047 A114048 A114049 KEYWORD easy,nonn AUTHOR Cino Hilliard, Feb 01 2006 EXTENSIONS More terms from Benoit Cloitre, Feb 03 2006 a(11) and a(12) from Harvey P. Dale, Oct 22 2011 STATUS approved

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Last modified October 21 03:24 EDT 2019. Contains 328291 sequences. (Running on oeis4.)