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A083105 Second-order linear recurrence sequence with a(n) = a(n-1) + a(n-2). 4
62638280004239857, 49463435743205655, 112101715747445512, 161565151490651167, 273666867238096679, 435232018728747846, 708898885966844525, 1144130904695592371, 1853029790662436896 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

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.

REFERENCES

R. L. Graham, Math. Mag. 37, 1964, pp. 322-324.

D. E. Knuth, Math. Mag. 63, 1990, pp. 21-25.

LINKS

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

Tanya Khovanova, Recursive Sequences

J. W. Nicol, A Fibonacci-like sequence of composite numbers

Prime Puzzles, Problem 31. Fibonacci- all composites sequence

Index to sequences with linear recurrences with constant coefficients, signature (1,1).

FORMULA

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

CROSSREFS

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

Sequence in context: A204189 A051167 A155057 * A246287 A115499 A104837

Adjacent sequences:  A083102 A083103 A083104 * A083106 A083107 A083108

KEYWORD

nonn,easy

AUTHOR

Harry J. Smith, Apr 23 2003

STATUS

approved

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Last modified September 1 09:46 EDT 2014. Contains 246289 sequences.