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
Seiichi Manyama, Table of n, a(n) for n = 0..4705
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.
Index entries for linear recurrences with constant coefficients, signature (1,1).
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
KEYWORD
nonn,easy
AUTHOR
Harry J. Smith, Apr 23 2003
STATUS
approved