

A114046


Numbers x such that x^2  92*y^2 = 1.


1



1, 1151, 2649601, 6099380351, 14040770918401, 32321848554778751, 74404881332329766401, 171280004505174567476351, 394286495966030522000793601, 907647342433797756471259393151, 2089403787996106469366317122240001, 4809806612319694658683505544137089151
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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 [598668] 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(n1)a(n2)  Benoit Cloitre, Feb 03 2006
G.f.: (11151x)/(12302x+x^2). [From Philippe Deléham, Nov 18 2008]
a(n)=1/2*{[1151240*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*a1a0; 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



