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A082411
Second-order linear recurrence sequence with a(n) = a(n-1) + a(n-2), with initial terms 407389224418, 76343678551.
8
407389224418, 76343678551, 483732902969, 560076581520, 1043809484489, 1603886066009, 2647695550498, 4251581616507, 6899277167005, 11150858783512, 18050135950517, 29200994734029, 47251130684546, 76452125418575, 123703256103121, 200155381521696, 323858637624817
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
Arturas Dubickas, Aivaras Novikas and 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.
D. Ismailescu and J. Son, A New Kind of Fibonacci-Like Sequence of Composite Numbers, J. Int. Seq. 17 (2014) # 14.8.2.
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.
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
MATHEMATICA
LinearRecurrence[{1, 1}, {407389224418, 76343678551}, 25] (* Paolo Xausa, Nov 07 2023 *)
CROSSREFS
Cf. A000032 (Lucas numbers), A000045 (Fibonacci numbers), A083103, A083104, A083105, A083216, A221286.
Sequence in context: A387154 A357687 A363799 * A113952 A375647 A218865
KEYWORD
nonn,easy
AUTHOR
Harry J. Smith, Apr 23 2003
EXTENSIONS
Name clarified by Robert C. Lyons, Feb 07 2025
STATUS
approved