This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A041923 #28 Feb 16 2025 08:32:38
%S A041923 1,1,43,44,1891,1935,83161,85096,3657193,3742289,160833331,164575620,
%T A041923 7073009371,7237584991,311051578993,318289163984,13679196466321,
%U A041923 13997485630305,601573592939131,615571078569436,26455558892855443,27071129971424879
%N A041923 Denominators of continued fraction convergents to sqrt(483).
%C A041923 The following remarks assume an offset of 1. This is the sequence of Lehmer numbers U_n(sqrt(R),Q) for the parameters R = 42 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
%H A041923 Vincenzo Librandi, <a href="/A041923/b041923.txt">Table of n, a(n) for n = 0..200</a>
%H A041923 Eric W. Weisstein, <a href="https://mathworld.wolfram.com/LehmerNumber.html">MathWorld: Lehmer Number</a>
%H A041923 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,44,0,-1).
%F A041923 G.f.: -(x^2 -x -1) / (x^4 -44*x^2 +1). - _Colin Barker_, Nov 27 2013
%F A041923 a(n) = 44*a(n-2) - a(n-4) for n > 3. - _Vincenzo Librandi_, Dec 27 2013
%F A041923 From _Peter Bala_, May 27 2014: (Start)
%F A041923 The following remarks assume an offset of 1.
%F A041923 Let alpha = ( sqrt(42) + sqrt(46) )/2 and beta = ( sqrt(42) - sqrt(46) )/2 be the roots of the equation x^2 - sqrt(42)*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.
%F A041923 a(n) = Product_{k = 1..floor((n-1)/2)} ( 42 + 4*cos^2(k*Pi/n) ).
%F A041923 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) = 42*a(2*n) + a(2*n - 1). (End)
%t A041923 Denominator[Convergents[Sqrt[483], 30]] (* _Vincenzo Librandi_, Dec 27 2013 *)
%o A041923 (Magma) I:=[1,1,43,44]; [n le 4 select I[n] else 44*Self(n-2)-Self(n-4): n in [1..30]]; // _Vincenzo Librandi_, Dec 27 2013
%Y A041923 Cf. A041922, A176400, A040461, A002530.
%K A041923 nonn,frac,easy
%O A041923 0,3
%A A041923 _N. J. A. Sloane_
%E A041923 More terms from _Colin Barker_, Nov 27 2013