The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A042199 Denominators of continued fraction convergents to sqrt(624). 2
 1, 1, 49, 50, 2449, 2499, 122401, 124900, 6117601, 6242501, 305757649, 312000150, 15281764849, 15593764999, 763782484801, 779376249800, 38173842475201, 38953218725001, 1907928341275249, 1946881560000250, 95358243221287249, 97305124781287499 (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 = 48 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 27 2014 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..100 Eric W. Weisstein, MathWorld: Lehmer Number Index entries for linear recurrences with constant coefficients, signature (0,50,0,-1). FORMULA G.f.: -(x^2-x-1) / (x^4-50*x^2+1). - Colin Barker, Nov 19 2013 From Peter Bala, May 27 2014: (Start) The following remarks assume an offset of 1. Let alpha = sqrt(12) + sqrt(13) and beta = sqrt(12) - sqrt(13) be the roots of the equation x^2 - sqrt(48)*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)} ( 48 + 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) = 48*a(2*n) + a(2*n - 1). (End) MATHEMATICA Denominator[Convergents[Sqrt[624], 30]] (* Harvey P. Dale, Sep 22 2013 *) CROSSREFS Cf. A042198, A040599. A002530. Sequence in context: A037412 A176309 A080201 * A257443 A020276 A118073 Adjacent sequences:  A042196 A042197 A042198 * A042200 A042201 A042202 KEYWORD nonn,frac,easy AUTHOR EXTENSIONS More terms from Colin Barker, Nov 19 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 January 18 08:37 EST 2021. Contains 340250 sequences. (Running on oeis4.)