%I #47 Nov 07 2023 12:55:27
%S 20615674205555510,3794765361567513,24410439567123023,
%T 28205204928690536,52615644495813559,80820849424504095,
%U 133436493920317654,214257343344821749,347693837265139403,561951180609961152,909645017875100555,1471596198485061707,2381241216360162262
%N Fibonacci-like sequence of composite numbers with a(0) = 20615674205555510, a(1) = 3794765361567513.
%C a(0) = 20615674205555510, a(1) = 3794765361567513. This is a second-order linear recurrence sequence with a(0) and a(1) coprime that does not contain any primes. It was found by Herbert S. Wilf in 1990.
%H Seiichi Manyama, <a href="/A083216/b083216.txt">Table of n, a(n) for n = 0..4709</a> (terms 0..1000 from Alois P. Heinz)
%H Arturas Dubickas, Aivaras Novikas and Jonas Šiurys, <a href="http://dx.doi.org/10.1016/j.jnt.2010.03.015">A binary linear recurrence sequence of composite numbers</a>, Journal of Number Theory, Volume 130, Issue 8, August 2010, Pages 1737-1749.
%H R. L. Graham, <a href="http://www.jstor.org/stable/2689243">A Fibonacci-Like sequence of composite numbers</a>, Math. Mag. 37 (1964) 322-324
%H D. Ismailescu and J. Son, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL17/Ismailescu/ism8.html">A New Kind of Fibonacci-Like Sequence of Composite Numbers</a>, J. Int. Seq. 17 (2014) # 14.8.2.
%H Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H D. E. Knuth, <a href="http://www.jstor.org/stable/2691504">A Fibonacci-Like sequence of composite numbers</a>, Math. Mag. 63 (1) (1990) 21-25
%H J. W. Nicol, <a href="https://doi.org/10.37236/1476">A Fibonacci-like sequence of composite numbers</a>, The Electronic Journal of Combinatorics, Volume 6 (1999), Research Paper #R44.
%H Herbert S. Wilf, <a href="http://www.jstor.org/stable/2690956">Letters to the Editor</a>, Math. Mag. 63, 284, 1990.
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (1,1).
%F a(n) = a(n-1) + a(n-2) for n>1.
%F G.f.: (20615674205555510-16820908843987997*x)/(1-x-x^2).
%p a:= n-> (<<0|1>, <1|1>>^n. <<20615674205555510, 3794765361567513>>)[1, 1]:
%p seq(a(n), n=0..20); # _Alois P. Heinz_, Apr 04 2013
%t LinearRecurrence[{1,1},{20615674205555510,3794765361567513},25] (* _Paolo Xausa_, Nov 07 2023 *)
%o (PARI) Vec((20615674205555510-16820908843987997*x)/(1-x-x^2)+O(x^9)) \\ _Charles R Greathouse IV_, Sep 23 2012
%Y Cf. A000032, A000045, A083103, A083104, A083105, A082411, A221286.
%K nonn,easy
%O 0,1
%A _Harry J. Smith_, Apr 23 2003