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A082411 Second-order linear recurrence sequence with a(n) = a(n-1) + a(n-2). 5
407389224418, 76343678551, 483732902969, 560076581520, 1043809484489, 1603886066009, 2647695550498, 4251581616507, 6899277167005, 11150858783512, 18050135950517, 29200994734029, 47251130684546, 76452125418575, 123703256103121, 200155381521696, 323858637624817 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

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.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Arturas Dubickas, Aivaras Novikas, Jonas Šiurys, A binary linear recurrence sequence of composite numbers, Journal of Number Theory, Volume 130, Issue 8, August 2010, Pages 1737-1749.

R. L. Graham, A Fibonacci-Like sequence of composite numbers, Math. Mag. 37 (1964) 322-324.

Tanya Khovanova, Recursive Sequences

D. E. Knuth, A Fibonacci-Like sequence of composite numbers, Math. Mag. 63 (1) (1990) 21-25

J. W. Nicol, A Fibonacci-like sequence of composite numbers, The Electronic Journal of Combinatorics, Volume 6 (1999), Research Paper #R44.

Herbert S. Wilf, Letters to the Editor Math. Mag. 63, 284, 1990.

Index entries for linear recurrences with constant coefficients, signature (1,1).

FORMULA

G.f.: (407389224418-331045545867*x)/(1-x-x^2). [Colin Barker, Jun 19 2012]

MAPLE

a:= n-> (<<0|1>, <1|1>>^n. <<407389224418, 76343678551>>)[1, 1]:

seq(a(n), n=0..20);  # Alois P. Heinz, Apr 04 2013

CROSSREFS

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

Sequence in context: A080132 A080122 A269417 * A113952 A218865 A209833

Adjacent sequences:  A082408 A082409 A082410 * A082412 A082413 A082414

KEYWORD

nonn,easy

AUTHOR

Harry J. Smith, Apr 23 2003

STATUS

approved

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Last modified July 24 04:36 EDT 2016. Contains 274964 sequences.