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A082916 Numbers k such that k and binomial(2*k, k) are relatively prime. 3
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 (list; graph; refs; listen; history; text; internal format)
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: A323550 A165468 A112372 * A325372 A098903 A061345

Adjacent sequences:  A082913 A082914 A082915 * A082917 A082918 A082919

KEYWORD

nonn

AUTHOR

Benoit Cloitre, May 25 2003

STATUS

approved

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Last modified June 21 10:09 EDT 2021. Contains 345360 sequences. (Running on oeis4.)