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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. Index entries for linear recurrences with constant coefficients, signature (1,1). 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 PROG (PARI) Vec((20615674205555510-16820908843987997*x)/(1-x-x^2)+O(x^9)) \\ Charles R Greathouse IV, Sep 23 2012 CROSSREFS Cf. A000032, A000045, A083103, A083104, A083105, A082411, A221286. Sequence in context: A172655 A288287 A349030 * A180703 A336967 A338959 Adjacent sequences: A083213 A083214 A083215 * A083217 A083218 A083219 KEYWORD nonn,easy AUTHOR Harry J. Smith, Apr 23 2003 STATUS approved

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Last modified March 29 15:25 EDT 2023. Contains 361599 sequences. (Running on oeis4.)