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

1,1

Links

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

Formula

From Antti Karttunen, Apr 17 2015: (Start)

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

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

(End)

Example

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.

Mathematica

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

Prog

(Scheme, two alternative formulas)
(define (A008508 n) (+ -1 (A000720 (A071904 n))))
(define (A008508 n) (- (A053726 n) n 1))
;; Antti Karttunen, 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

Crossrefs

Cf. A000720, A053726, A071904, A111333.

Sequence in context: A218490 A161696 A196084 * A163301 A036593 A086674

Adjacent sequences: A008505 A008506 A008507 * A008509 A008510 A008511

Keyword

nonn

Author

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

Status

approved