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Number of odd numbers <= n-th prime.
15

%I #22 Aug 02 2024 19:52:33

%S 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,

%T 51,52,54,55,57,64,66,69,70,75,76,79,82,84,87,90,91,96,97,99,100,106,

%U 112,114,115,117,120,121,126,129,132,135,136,139,141,142,147,154,156,157

%N Number of odd numbers <= n-th prime.

%C 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

%C Same as smallest k such that prime(n) divides C(2k,k). - _Jonathan Sondow_, Jan 20 2016

%C Positions of records in A046112. - _Hugo Pfoertner_, Jul 11 2019

%H Ray Chandler, <a href="/A111333/b111333.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = ceiling((prime_n)/2). - _Robert G. Wilson v_, Nov 07 2005

%p seq(ceil(ithprime(i)/2), i=1..100); # _Robert Israel_, Jan 20 2016

%t Table[ Ceiling[ Prime[n]/2], {n, 65}] (* _Robert G. Wilson v_ *)

%o (PARI) a(n)=(prime(n)+1)\2 \\ _Charles R Greathouse IV_, Sep 16 2015

%o (Python)

%o from sympy import prime

%o def A111333(n): return prime(n)+1>>1 # _Chai Wah Wu_, Aug 02 2024

%Y Cf. A006254, A046112, A049990, A062875.

%K nonn,easy

%O 1,2

%A _Giovanni Teofilatto_, Nov 05 2005

%E More terms from _Robert G. Wilson v_, Nov 07 2005