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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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois Alcover, Jun 07 2020 *)

CROSSREFS

Cf. A000045, A001602.

Sequence in context: A201362 A063976 A064000 * A253898 A173135 A020627

Adjacent sequences:  A069177 A069178 A069179 * A069181 A069182 A069183

KEYWORD

easy,nonn

AUTHOR

Benoit Cloitre, Apr 10 2002

STATUS

approved

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Last modified September 25 18:21 EDT 2020. Contains 337344 sequences. (Running on oeis4.)