A114046 Numbers x such that x^2 - 92*y^2 = 1 for some y.

1, 1151, 2649601, 6099380351, 14040770918401, 32321848554778751, 74404881332329766401, 171280004505174567476351, 394286495966030522000793601, 907647342433797756471259393151, 2089403787996106469366317122240001, 4809806612319694658683505544137089151

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

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: A098976 A351679 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