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 A114046 Numbers x such that x^2 - 92*y^2 = 1 for some y. 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 Bob Jacobs, The Nature of Mathematics and Mathematicians 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). - Philippe Deléham, Nov 18 2008 a(n) = (1/2)*((1151-240*sqrt(23))^n + (1151+240*sqrt(23))^n), with n >= 0. - Paolo P. Lava, Nov 24 2008 EXAMPLE 1151^2 - 92 * 120^2 = 1, so 1151 is a term. 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, ", ")) \\ Benoit Cloitre, Feb 03 2006 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 29 21:59 EDT 2020. Contains 338074 sequences. (Running on oeis4.)