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A083104 Second-order linear recurrence sequence with a(n) = a(n-1) + a(n-2). 6
331635635998274737472200656430763, 1510028911088401971189590305498785, 1841664547086676708661790961929548, 3351693458175078679851381267428333, 5193358005261755388513172229357881, 8545051463436834068364553496786214 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

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 Ronald Graham in 1964.

LINKS

Indranil Ghosh, Table of n, a(n) for n = 0..4618

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).

FORMULA

G.f.: (331635635998274737472200656430763+1178393275090127233717389649068022*x)/(1-x-x^2). - Colin Barker, Jun 19 2012

MATHEMATICA

LinearRecurrence[{1, 1}, {331635635998274737472200656430763, 1510028911088401971189590305498785}, 7] (* Harvey P. Dale, Oct 29 2016 *)

PROG

(PARI) a(n)=331635635998274737472200656430763*fibonacci(n-1)+ 1510028911088401971189590305498785*fibonacci(n) \\ Charles R Greathouse IV, Dec 18 2014

CROSSREFS

Cf. A000032 (Lucas numbers), A000045 (Fibonacci numbers), A083103, A083105, A083216, A082411.

Sequence in context: A120318 A095458 A277140 * A115531 A095460 A083103

Adjacent sequences:  A083101 A083102 A083103 * A083105 A083106 A083107

KEYWORD

nonn,easy

AUTHOR

Harry J. Smith, Apr 23 2003

STATUS

approved

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Last modified March 22 22:17 EDT 2017. Contains 283901 sequences.