

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: A353124 A354149 A112372 * A325372 A098903 A061345
Adjacent sequences: A082913 A082914 A082915 * A082917 A082918 A082919


KEYWORD

nonn


AUTHOR

Benoit Cloitre, May 25 2003


STATUS

approved



