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
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