This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A041263 Denominators of continued fraction convergents to sqrt(143). 2
 1, 1, 23, 24, 551, 575, 13201, 13776, 316273, 330049, 7577351, 7907400, 181540151, 189447551, 4349386273, 4538833824, 104203730401, 108742564225, 2496540143351, 2605282707576, 59812759710023, 62418042417599, 1433009692897201, 1495427735314800 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS The following remarks assume an offset of 1. This is the sequence of Lehmer numbers U_n(sqrt(R),Q) for the parameters R = 22 and Q = -1; it is a strong divisibility sequence, that is, GCD(a(n),a(m)) = a(GCD(n,m)) for all positive integers n and m. Consequently, this is a divisibility sequence: if n divides m then a(n) divides a(m). - Peter Bala, May 28 2014 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..200 Eric W. Weisstein, MathWorld: Lehmer Number Index entries for linear recurrences with constant coefficients, signature (0,24,0,-1). FORMULA G.f.: (1 +x -x^2)/(x^4 -24*x^2 +1). - Vincenzo Librandi, Dec 14 2013 a(n) = 24*a(n-2) - a(n-4). - Vincenzo Librandi, Dec 14 2013 From Peter Bala, May 28 2014: (Start) The following remarks assume an offset of 1. Let alpha = ( sqrt(22) + sqrt(26) )/2 and beta = ( sqrt(22) - sqrt(26) )/2 be the roots of the equation x^2 - sqrt(22)*x - 1 = 0. Then a(n) = (alpha^n - beta^n)/(alpha - beta) for n odd, while a(n) = (alpha^n - beta^n)/(alpha^2 - beta^2) for n even. a(n) = product {k = 1..floor((n-1)/2)} ( 22 + 4*cos^2(k*Pi/n) ). Recurrence equations: a(0) = 0, a(1) = 1 and for n >= 1, a(2*n) = a(2*n - 1) + a(2*n - 2) and a(2*n + 1) = 22*a(2*n) + a(2*n - 1). (End) MATHEMATICA Denominator[Convergents[Sqrt[143], 30]] (* or *) CoefficientList[Series[(1 + x - x^2)/(x^4 - 24 x^2 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 14 2013 *) PROG (MAGMA) I:=[1, 1, 23, 24]; [n le 4 select I[n] else 24*Self(n-2)-Self(n-4): n in [1..40]]; // Vincenzo Librandi, Dec 14 2013 CROSSREFS Cf. A041262, A002530. Sequence in context: A042094 A042096 A042098 * A042100 A042101 A042102 Adjacent sequences:  A041260 A041261 A041262 * A041264 A041265 A041266 KEYWORD nonn,frac,easy,less AUTHOR EXTENSIONS More terms from Vincenzo Librandi, Dec 14 2013 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified March 20 09:35 EDT 2019. Contains 321345 sequences. (Running on oeis4.)