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%I #38 Nov 07 2023 12:55:42
%S 407389224418,76343678551,483732902969,560076581520,1043809484489,
%T 1603886066009,2647695550498,4251581616507,6899277167005,
%U 11150858783512,18050135950517,29200994734029,47251130684546,76452125418575,123703256103121,200155381521696,323858637624817
%N Second-order linear recurrence sequence with a(n) = a(n-1) + a(n-2).
%C a(0) = 407389224418, a(1) = 76343678551. 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 John Nicol in 1999.
%H Alois P. Heinz, <a href="/A082411/b082411.txt">Table of n, a(n) for n = 0..1000</a>
%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 G.f.: (407389224418-331045545867*x)/(1-x-x^2). [_Colin Barker_, Jun 19 2012]
%p a:= n-> (<<0|1>, <1|1>>^n. <<407389224418, 76343678551>>)[1, 1]:
%p seq(a(n), n=0..20); # _Alois P. Heinz_, Apr 04 2013
%t LinearRecurrence[{1,1},{407389224418,76343678551},25] (* _Paolo Xausa_, Nov 07 2023 *)
%Y Cf. A000032 (Lucas numbers), A000045 (Fibonacci numbers), A083103, A083104, A083105, A083216, A221286.
%K nonn,easy
%O 0,1
%A _Harry J. Smith_, Apr 23 2003
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