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A177412 Fibonacci sequence beginning 14831,41069. 1
14831, 41069, 55900, 96969, 152869, 249838, 402707, 652545, 1055252, 1707797, 2763049, 4470846, 7233895, 11704741, 18938636, 30643377, 49582013, 80225390, 129807403, 210032793, 339840196, 549872989, 889713185, 1439586174, 2329299359, 3768885533, 6098184892, 9867070425, 15965255317, 25832325742, 41797581059 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

a(0)=14831 is a prime; the next prime number in the sequence is a(18604) = 2278143...6069, which has 3893 digits. (The initial values are chosen for this particularly long chain of consecutive composites.)

LINKS

Colin Barker, Table of n, a(n) for n = 0..1000

D. E. Knuth, A Fibonacci-like sequence of composite numbers, Math. Mag. 63 (1) (1990) 21-25.

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

FORMULA

From R. J. Mathar, Dec 12 2010: (Start)

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

G.f.: (14831+26238*x) / (1-x-x^2).

(End)

a(n) = (2^(-1-n)*((1-sqrt(5))^n*(-67307+14831*sqrt(5)) + (1+sqrt(5))^n*(67307+14831*sqrt(5)))) / sqrt(5). - Colin Barker, May 03 2017

MATHEMATICA

q=2; Do[Do[If[GCD[x, y]!=1, Break[]]; a=x; b=y; lst={a, b}; k=2; Do[If[PrimeQ[c=a+b], Break[]]; k++; AppendTo[lst, c]; a=b; b=c, {n, 10!}]; If[k>q, q=k; Print[If[Length[lst]>9, Take[lst, 9], lst], k, "=", c]], {y, 2*x+1, 4*x+1}], {x, 0, 10!}]

PROG

(PARI) Vec((14831+26238*x) / (1-x-x^2) + O(x^30)) \\ Colin Barker, May 03 2017

CROSSREFS

Cf. A000045.

Sequence in context: A251332 A186790 A234766 * A209947 A023045 A186901

Adjacent sequences:  A177409 A177410 A177411 * A177413 A177414 A177415

KEYWORD

nonn,easy

AUTHOR

Vladimir Joseph Stephan Orlovsky, Dec 10 2010

STATUS

approved

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Last modified August 18 08:57 EDT 2019. Contains 326077 sequences. (Running on oeis4.)