login
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
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.)
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
KEYWORD
nonn,easy
AUTHOR
STATUS
approved