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A083216 Fibonacci-like sequence of composite numbers with a(0) = 20615674205555510, a(1) = 3794765361567513. 8
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, 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, 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.

Sequence in context: A185434 A172655 A288287 * A180703 A145065 A080127

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 December 10 12:33 EST 2018. Contains 318047 sequences. (Running on oeis4.)