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A082411 Second-order linear recurrence sequence with a(n) = a(n-1) + a(n-2). 4


%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.

%D R. L. Graham, Math. Mag. 37, 1964, pp. 322-324.

%D D. E. Knuth, Math. Mag. 63, 1990, pp. 21-25.

%D H. S. Wilf, Letters to the Editor, Math. Mag. 63, 1990.

%H Alois P. Heinz, <a href="/A082411/b082411.txt">Table of n, a(n) for n = 0..1000</a>

%H Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>

%H J. W. Nicol, <a href="http://www.combinatorics.org/Volume_6/PostScriptfiles/v6i1r44.ps">A Fibonacci-like sequence of composite numbers</a>

%H <a href="/index/Rea#recLCC">Index to sequences with 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

%Y Cf. A000032 (Lucas numbers), A000045 (Fibonacci numbers), A083103, A083104, A083105, A083216.

%K nonn,easy

%O 0,1

%A _Harry J. Smith_, Apr 23 2003

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Last modified December 19 15:14 EST 2014. Contains 252230 sequences.