A008508 Number of odd primes less than n-th odd composite number.

3, 5, 7, 8, 8, 10, 10, 11, 13, 14, 14, 15, 15, 17, 17, 18, 20, 20, 21, 22, 22, 23, 23, 23, 24, 26, 28, 29, 29, 29, 29, 29, 29, 30, 31, 31, 33, 33, 33, 33, 35, 35, 36, 36, 37, 38, 38, 39, 39, 41, 41, 41, 41, 43, 45, 45, 45, 45, 45, 46

Offset: 1

Author

Gary Findley (chfindley(AT)alpha.nlu.edu), Mar 15 1996

Keywords

• nonn

Examples

			The first odd composite is 9, and there are 4 primes below: 2, 3, 5, and 7; so there are 3 odd primes, hence a(1)=3.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000720, A053726, A071904, A111333.

Programs

Mathematica

PrimePi[#] - 1 & /@ Select[Range@ 213, CompositeQ@ # && OddQ@ # &] (* Michael De Vlieger, Apr 17 2015 *)

PARI

lista(nn) = {forcomposite (n=1, nn, if (n % 2, print1(primepi(n)-1, ", ")););} \\ Michel Marcus, Apr 18 2015

Python

from sympy import primepi
def A008508(n):
    if n == 1: return 3
    m, k = n, (r:=primepi(n)) + n + (n>>1)
    while m != k:
        m, k = k, (r:=primepi(k)) + n + (k>>1)
    return r-1 # Chai Wah Wu, Aug 01 2024

Formula

From Antti Karttunen, Apr 17 2015: (Start)

a(n) = A000720(A071904(n)) - 1 (by the definition).

a(n) = A053726(n) - n - 1.

(End)