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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)



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.


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.

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.

Prime Puzzles, Problem 31. Fibonacci- all composites sequence

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


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


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


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


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




Harry J. Smith, Apr 23 2003



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Last modified December 18 08:16 EST 2018. Contains 318219 sequences. (Running on oeis4.)