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A083105
Second-order linear recurrence sequence with a(n) = a(n-1) + a(n-2).
9
62638280004239857, 49463435743205655, 112101715747445512, 161565151490651167, 273666867238096679, 435232018728747846, 708898885966844525, 1144130904695592371, 1853029790662436896, 2997160695358029267, 4850190486020466163, 7847351181378495430
OFFSET
0,1
COMMENTS
a(0) = 62638280004239857, a(1) = 49463435743205655. 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 D. E. Knuth in 1990.
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.
Carlos Rivera, Problem 31. Fibonacci- all composites sequence, The Prime Puzzles and Problems Connection.
FORMULA
G.f.: (62638280004239857-13174844261034202*x)/(1-x-x^2). [Colin Barker, Jun 19 2012]
MAPLE
a:= n-> (<<0|1>, <1|1>>^n. <<62638280004239857, 49463435743205655>>)[1, 1]:
seq(a(n), n=0..20); # Alois P. Heinz, Sep 20 2021
MATHEMATICA
LinearRecurrence[{1, 1}, {62638280004239857, 49463435743205655}, 20] (* Paolo Xausa, Nov 07 2023 *)
CROSSREFS
Cf. A000032 (Lucas numbers), A000045 (Fibonacci numbers), A083103, A083104, A083216, A082411, A221286.
Sequence in context: A329223 A317164 A338443 * A246287 A115499 A257168
KEYWORD
nonn,easy
AUTHOR
Harry J. Smith, Apr 23 2003
STATUS
approved