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A083216 Fibonacci-like sequence of composite numbers with a(0) = 20615674205555510, a(1) = 3794765361567513. 8
20615674205555510, 3794765361567513, 24410439567123023, 28205204928690536, 52615644495813559, 80820849424504095, 133436493920317654, 214257343344821749, 347693837265139403, 561951180609961152, 909645017875100555, 1471596198485061707, 2381241216360162262 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

a(0) = 20615674205555510, a(1) = 3794765361567513. 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 Herbert Wilf in 1990.

REFERENCES

H. S. Wilf, Letters to the Editor, Math. Mag. 63, 1990.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

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

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

FORMULA

a(n) = a(n-1) + a(n-2) for n>1.

G.f.: (20615674205555510-16820908843987997*x)/(1-x-x^2).

MAPLE

a:= n-> (<<0|1>, <1|1>>^n. <<20615674205555510, 3794765361567513>>)[1, 1]:

seq(a(n), n=0..20);  # Alois P. Heinz, Apr 04 2013

PROG

(PARI) Vec((20615674205555510-16820908843987997*x)/(1-x-x^2)+O(x^9)) \\ Charles R Greathouse IV, Sep 23 2012

CROSSREFS

Cf. A000032, A000045, A083103, A083104, A083105, A082411.

Sequence in context: A238358 A185434 A172655 * A180703 A145065 A080127

Adjacent sequences:  A083213 A083214 A083215 * A083217 A083218 A083219

KEYWORD

nonn,easy

AUTHOR

Harry J. Smith, Apr 23 2003

STATUS

approved

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Last modified November 24 02:09 EST 2014. Contains 249867 sequences.