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A083216 Fibonacci-like sequence of composite numbers with a(0) = 20615674205555510, a(1) = 3794765361567513. 11
20615674205555510, 3794765361567513, 24410439567123023, 28205204928690536, 52615644495813559, 80820849424504095, 133436493920317654, 214257343344821749, 347693837265139403, 561951180609961152, 909645017875100555, 1471596198485061707, 2381241216360162262 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
a(0) = 20615674205555510, a(1) = 3794765361567513. 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 Herbert S. Wilf in 1990.
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..4709 (terms 0..1000 from Alois P. Heinz)
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
a(n) = a(n-1) + a(n-2) for n>1.
G.f.: (20615674205555510-16820908843987997*x)/(1-x-x^2).
MAPLE
a:= n-> (<<0|1>, <1|1>>^n. <<20615674205555510, 3794765361567513>>)[1, 1]:
seq(a(n), n=0..20); # Alois P. Heinz, Apr 04 2013
MATHEMATICA
LinearRecurrence[{1, 1}, {20615674205555510, 3794765361567513}, 25] (* Paolo Xausa, Nov 07 2023 *)
PROG
(PARI) Vec((20615674205555510-16820908843987997*x)/(1-x-x^2)+O(x^9)) \\ Charles R Greathouse IV, Sep 23 2012
CROSSREFS
Sequence in context: A172655 A288287 A349030 * A180703 A336967 A338959
KEYWORD
nonn,easy
AUTHOR
Harry J. Smith, Apr 23 2003
STATUS
approved

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Last modified March 19 04:58 EDT 2024. Contains 370952 sequences. (Running on oeis4.)