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A083105 Second-order linear recurrence sequence with a(n) = a(n-1) + a(n-2). 6
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.


Seiichi Manyama, Table of n, a(n) for n = 0..4705

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 August 21 11:16 EDT 2017. Contains 290864 sequences.