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 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.
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
MATHEMATICA
LinearRecurrence[{1, 1}, {407389224418, 76343678551}, 25] (* Paolo Xausa, Nov 07 2023 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Harry J. Smith, Apr 23 2003
STATUS
approved