A111333 Number of odd numbers <= n-th prime.

1, 2, 3, 4, 6, 7, 9, 10, 12, 15, 16, 19, 21, 22, 24, 27, 30, 31, 34, 36, 37, 40, 42, 45, 49, 51, 52, 54, 55, 57, 64, 66, 69, 70, 75, 76, 79, 82, 84, 87, 90, 91, 96, 97, 99, 100, 106, 112, 114, 115, 117, 120, 121, 126, 129, 132, 135, 136, 139, 141, 142, 147, 154, 156, 157

Offset: 1

Author

Giovanni Teofilatto, Nov 05 2005

Keywords

• nonn
• easy

Comments

This is A006254 (numbers n such that 2n-1 is prime) with a leading 1. - Lambert Klasen (lambert.klasen(AT)gmx.net), Nov 06 2005

Same as smallest k such that prime(n) divides C(2k,k). - Jonathan Sondow, Jan 20 2016

Positions of records in A046112. - Hugo Pfoertner, Jul 11 2019

Links

• Ray Chandler, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A006254, A046112, A049990, A062875.

Programs

Maple

seq(ceil(ithprime(i)/2), i=1..100); # Robert Israel, Jan 20 2016

Mathematica

Table[ Ceiling[ Prime[n]/2], {n, 65}] (* Robert G. Wilson v, Nov 07 2005 *)

PARI

a(n)=(prime(n)+1)\2 \\ Charles R Greathouse IV, Sep 16 2015

Python

from sympy import prime
def A111333(n): return prime(n)+1>>1 # Chai Wah Wu, Aug 02 2024

Formula

a(n) = ceiling((prime_n)/2). - Robert G. Wilson v, Nov 07 2005

Extensions

More terms from Robert G. Wilson v, Nov 07 2005