OFFSET
1,2
COMMENTS
Sanna and Tron proved that a(n) is asymptotic to c*n, for some constant c > 0. - Carlo Sanna, May 11 2017
For k from 1 to 9, a(10^k) is equal to 14, 154, 1553, 15578, 155786, 1557934, 15579574, 155796106, 1557962159. - Giovanni Resta, May 11 2017
The asymptotic density of this sequence is Sum_{k>=1} mu(k)/lcm(k, A001177(k)), where mu is the Möbius function (A008683) (Sanna and Tron, 2018). - Amiram Eldar, Aug 07 2020
LINKS
Lars Blomberg, Table of n, a(n) for n = 1..10000
Carlo Sanna and Emanuele Tron, The density of numbers n having a prescribed G.C.D. with the nth Fibonacci number Indagationes Mathematicae, Vol. 29, No. 3 (2018), pp. 972-980, preprint, arXiv:1705.01805 [math.NT], 2017.
FORMULA
a(n) is probably asymptotic to c*n with c=1.55(8).....
MATHEMATICA
Select[Range[200], GCD[#, Fibonacci[#]] == 1 &] (* T. D. Noe, Jun 13 2012 *)
PROG
(PARI) isok(n) = gcd(n, fibonacci(n)) == 1; \\ Michel Marcus, May 05 2017
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Benoit Cloitre, Sep 17 2002
STATUS
approved