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 A086892 #31 Sep 08 2022 08:45:11
%S A086892 1,1,1,5,1,7,1,5,1,11,23,455,1,1,1,85,1,133,1,275,1,23,47,455,1,1,1,
%T A086892 145,1,2387,1,85,23,1,71,23350145,1,1,1,11275,1,2107,431,115,1,47,1,
%U A086892 750295,1,11,1,265,1,133,23,145,1,59,1,47322275,1,1,1,85,1,10787,1,5,47,781,1
%N A086892 Greatest common divisor of 2^n-1 and 3^n-1.
%C A086892 a(n) is a simple (the simplest?) example of a divisibility sequence associated to a rational point on an algebraic group of dimension larger than two. Specifically, it is the divisibility sequence associated to the point (2,3) on the two-dimensional torus G_m^2. Ailon and Rudnick conjecture that a(n) = 1 for infinitely many n.
%C A086892 According to Corvaja, a(n) < 2^n - 1 for all but finitely many n.
%D A086892 Y. Bugeaud, P. Corvaja, U. Zannier, An upper bound for the G.C.D. of a^n-1 and b^n-1. Math. Z. 243 (2003), no. 1, 79-84
%H A086892 Reinhard Zumkeller, <a href="/A086892/b086892.txt">Table of n, a(n) for n = 1..1000</a>
%H A086892 N. Ailon, Z. Rudnick, <a href="http://arXiv.org/abs/math/0202102">Torsion points on curves and common divisors of a^k-1 and b^k-1</a>, Acta Arith. 113 (2004), no. 1, 31-38.
%H A086892 Y. Bugeaud, P. Corvaja, U. Zannier, <a href="http://dx.doi.org/10.1007/s00209-002-0449-z">An upper bound for the G.C.D. of a^n-1 and b^n-1</a>, Math. Z. 243 (2003), no. 1, 79-84
%H A086892 P. Corvaja, <a href="http://atlas-conferences.com/cgi-bin/abstract/cbcw-70">Greatest Common Divisors in Vojta's Conjecture: Arithmetic and Geometry</a>, Journées Arithmétiques 2011.
%H A086892 <a href="/index/Di#divseq">Index to divisibility sequences</a>
%F A086892 a(n) = gcd(2^n - 1, 3^n - 1).
%F A086892 a(n) = GCD(A000255(n), A003462(n)) = GCD(A000255(n), A024023(n)). - _Reinhard Zumkeller_, Mar 26 2004
%p A086892 seq(igcd(2^n-1,3^n-1), n=1..100); # _Robert Israel_, Sep 02 2015
%t A086892 Table[GCD[2^n - 1, 3^n - 1], {n, 100}] (* _Vincenzo Librandi_, Sep 02 2015 *)
%o A086892 (PARI) vector(100,n,gcd(2^n-1,3^n-1))
%o A086892 (Haskell)
%o A086892 a086892 n = a086892_list !! (n-1)
%o A086892 a086892_list = tail $ zipWith gcd a000225_list a003462_list
%o A086892 -- _Reinhard Zumkeller_, Jul 18 2015
%o A086892 (Magma) [Gcd(2^n-1, 3^n-1): n in [1..75]]; // _Vincenzo Librandi_, Sep 02 2015
%Y A086892 Cf. A000225, A000255, A003462, A024023, A260119.
%K A086892 easy,nonn
%O A086892 1,4
%A A086892 Joseph H. Silverman (jhs(AT)math.brown.edu), Sep 18 2003
%E A086892 Replaced arXiv URL with non-cached version by _R. J. Mathar_, Oct 23 2009