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A114051 x such that x^2 - 23*y^2 = 1. 4
1, 24, 1151, 55224, 2649601, 127125624, 6099380351, 292643131224, 14040770918401, 673664360952024, 32321848554778751, 1550775066268428024, 74404881332329766401, 3569883528885560359224, 171280004505174567476351, 8217870332719493678505624 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
A Pellian equation (Pell's equation). - Benoit Cloitre, Feb 03 2006
Numbers n such that 23*(n^2-1) is a square. - Vincenzo Librandi, Nov 13 2010
LINKS
Tanya Khovanova, Recursive Sequences
John Robertson, Home page.
FORMULA
a(0)=1, a(1)=24 then a(n) = 48*a(n-1)-a(n-2). - Benoit Cloitre, Feb 03 2006
G.f.: (1-24*x)/(1-48*x+x^2). - Philippe Deléham, Nov 18 2008
a(n) = T(n, 24) = (S(n, 48) - S(n-2, 48))/2, n >= 0, with Chebyshev's T- and S-polynomials (A049310 and A053120). - Wolfdieter Lang, Jul 02 2013
a(n) == 1 (mod 23). - Hugo Pfoertner, Feb 11 2024
MATHEMATICA
LinearRecurrence[{48, -1}, {1, 24}, 20] (* Harvey P. Dale, Aug 19 2022 *)
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=24; for(n=2, 30, a2=48*a1-a0; a0=a1; a1=a2; print1(a2, ", ")) \\ Benoit Cloitre, Feb 03 2006
(PARI) Vec((1-24*x)/(1-48*x+x^2) + O(x^20)) \\ Colin Barker, Jun 13 2015
(Magma) [n: n in [1..10000000] |IsSquare(23*(n^2-1))] - Vincenzo Librandi, Nov 13 2010
CROSSREFS
Sequence in context: A130552 A160260 A268149 * A269092 A010562 A080775
KEYWORD
easy,nonn
AUTHOR
Cino Hilliard, Feb 01 2006
EXTENSIONS
More terms from Benoit Cloitre, Feb 03 2006
More terms from Robert G. Wilson v, Mar 17 2006
STATUS
approved

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Last modified June 25 18:39 EDT 2024. Contains 373707 sequences. (Running on oeis4.)