OFFSET
1,2
COMMENTS
Are there any primes p >5 such that F(p) and p! are not relatively primes?
From Robert Israel, May 31 2018: (Start)
n is in the sequence if and only if there is no prime q = prime(k) <= n such that A001602(k) | n.
All primes > 5 are in the sequence, because A001602(k) < prime(k) for k > 3, and we can't have n prime unless A001602(k)=n.
(End)
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
FORMULA
Conjecture : a(n) = C*n*Log(n) + 0(n*Log(n)) with 0, 6 < C < 0, 7
MAPLE
N:= 200: # for all terms <= N
V:= Vector(N, 1):
F:= proc(n) option remember; procname(n-1)+procname(n-2) end proc:
F(0):= 0: F(1):= 1:
K:= proc(q) local k;
for k from 1 do if F(k) mod q = 0 then return k fi
od
end proc:
p:= 1:
do
p:= nextprime(p);
if p > N then break fi;
k:= K(p);
k0:= k*ceil(p/k);
V[[seq(i, i=k0..N, k)]]:= 0
od:
select(t -> V[t]=1, [$1..N]); # Robert Israel, May 31 2018
MATHEMATICA
Select[Range[1000], CoprimeQ[Fibonacci[#], #!]&] (* Jean-François Alcover, Jun 07 2020 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Benoit Cloitre, Apr 10 2002
STATUS
approved