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

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.

Sequence in context: A089409 A287269 A136988 * A292412 A113733 A294434

Adjacent sequences: A074722 A074723 A074724 * A074726 A074727 A074728

Keyword

nonn

Author

Benoit Cloitre, Sep 04 2002

Status

approved