A177412 Fibonacci sequence beginning 14831,41069.

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

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

Maple

a:= n-> (<<0|1>, <1|1>>^n. <<14831, 41069>>)[1, 1]:
seq(a(n), n=0..30);  # Alois P. Heinz, Oct 06 2021

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