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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
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
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
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