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A083105 Second-order linear recurrence sequence with a(n) = a(n-1) + a(n-2). 5
62638280004239857, 49463435743205655, 112101715747445512, 161565151490651167, 273666867238096679, 435232018728747846, 708898885966844525, 1144130904695592371, 1853029790662436896 (list; graph; refs; listen; history; text; internal format)



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.


Table of n, a(n) for n=0..8.

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.

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.

Prime Puzzles, Problem 31. Fibonacci- all composites sequence

Index entries for linear recurrences with constant coefficients, signature (1,1).


G.f.: (62638280004239857-13174844261034202*x)/(1-x-x^2). [Colin Barker, Jun 19 2012]


Cf. A000032 (Lucas numbers), A000045 (Fibonacci numbers), A083103, A083104, A083216, A082411.

Sequence in context: A204189 A051167 A155057 * A246287 A115499 A257168

Adjacent sequences:  A083102 A083103 A083104 * A083106 A083107 A083108




Harry J. Smith, Apr 23 2003



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Last modified December 10 23:13 EST 2016. Contains 279021 sequences.