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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 Colin Barker, Table of n, a(n) for n = 0..594 Tanya Khovanova, Recursive Sequences John Robertson, Home page. Index entries for sequences related to Chebyshev polynomials. Index entries for linear recurrences with constant coefficients, signature (48,-1). 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 Adjacent sequences: A114048 A114049 A114050 * A114052 A114053 A114054 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.)