A082916 Numbers k such that k and binomial(2*k, k) are relatively prime.

0, 1, 3, 5, 7, 9, 11, 13, 17, 19, 23, 25, 27, 29, 31, 37, 39, 41, 43, 47, 49, 53, 55, 59, 61, 67, 71, 73, 79, 81, 83, 89, 93, 97, 101, 103, 107, 109, 111, 113, 119, 121, 125, 127, 131, 137, 139, 149, 151, 155, 157, 161, 163, 167, 169, 173, 179, 181, 185, 191, 193, 197

Offset

1,3

Links

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Formula

It seems that a(n) is asymptotic to c*n*log(n) with 0.7<c<0.8.

Mathematica

Select[Range[0, 100], CoprimeQ[Binomial[2*#, #], #] &] (* Amiram Eldar, May 24 2020 *)

Prog

(PARI) isok(n) = gcd(n, binomial(2*n, n)) == 1; \\ Michel Marcus, Dec 04 2013
(Python)
from __future__ import division
from fractions import gcd
A082916_list, b = [], 1
for n in range(10**5):
    if gcd(n, b) == 1:
        A082916_list.append(n)
    b = b*(4*n+2)//(n+1) # Chai Wah Wu, Mar 25 2016

Crossrefs

Cf. A000984 (central binomial coefficients).

Sequence in context: A354149 A371533 A112372 * A325372 A098903 A061345

Adjacent sequences: A082913 A082914 A082915 * A082917 A082918 A082919

Keyword

nonn

Author

Benoit Cloitre, May 25 2003

Status

approved