A074725 - OEIS

A074725

Numbers k such that F(k) and C(2k,k) are relatively prime, where F(k) is the k-th Fibonacci number (A000045(k)).

1, 2, 4, 5, 11, 13, 14, 17, 22, 23, 25, 26, 29, 31, 34, 38, 41, 43, 46, 47, 53, 59, 61, 62, 67, 71, 73, 74, 82, 83, 86, 89, 94, 101, 103, 106, 107, 109, 113, 118, 121, 122, 125, 127, 131, 134, 137, 142, 146, 149, 151, 155, 158, 163, 166, 167, 173, 175, 179, 181

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000

Amiram Eldar, Plot of a(n)/(n*log(log(n))) for n = 3..100000

FORMULA

It seems that a(n) is asymptotic to c*n*log(log(n)) with 2.1 < c < 2.3.

MATHEMATICA

Select[Range[200], CoprimeQ[Fibonacci[#], Binomial[2*#, #]] &] (* Amiram Eldar, May 08 2022 *)

CROSSREFS

Cf. A000045, A000984.