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URL: https://oeis.org/A069180

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A069180
F(n) and n! are relatively prime where F(n) are the Fibonacci numbers.
4
1, 2, 7, 11, 13, 17, 19, 22, 23, 26, 29, 31, 34, 37, 41, 43, 46, 47, 53, 58, 59, 61, 62, 67, 71, 73, 79, 82, 83, 86, 89, 94, 97, 101, 103, 106, 107, 109, 113, 118, 122, 127, 131, 134, 137, 139, 142, 146, 149, 151, 157, 163, 166, 167, 169, 173, 178, 179, 181, 191
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
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
Sequence in context: A201362 A063976 A064000 * A253898 A173135 A020627
KEYWORD
easy,nonn
AUTHOR
Benoit Cloitre, Apr 10 2002
STATUS
approved