A074215 - OEIS

A074215

Numbers m such that m and F(m) are relatively prime, where F(m) denotes the m-th Fibonacci number.

1, 2, 3, 4, 7, 8, 9, 11, 13, 14, 16, 17, 19, 21, 22, 23, 26, 27, 28, 29, 31, 32, 33, 34, 37, 38, 39, 41, 43, 44, 46, 47, 49, 51, 52, 53, 57, 58, 59, 61, 62, 63, 64, 67, 68, 69, 71, 73, 74, 76, 77, 79, 81, 82, 83, 86, 87, 88, 89, 92, 93, 94, 97, 98, 99, 101

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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

Cf. A000045, A001177, A008683, A104714.

Sequence in context: A167055 A022162 A022164 * A145487 A061856 A105941

Adjacent sequences: A074212 A074213 A074214 * A074216 A074217 A074218

KEYWORD

easy,nonn

AUTHOR

Benoit Cloitre, Sep 17 2002

STATUS

approved