A098592 Number of primes between n*30 and (n+1)*30.

10, 7, 7, 6, 5, 6, 5, 6, 5, 5, 4, 6, 5, 4, 6, 5, 5, 2, 5, 5, 5, 6, 4, 4, 4, 5, 3, 6, 4, 4, 4, 4, 4, 5, 5, 4, 6, 3, 3, 4, 5, 4, 4, 6, 2, 3, 3, 5, 4, 7, 2, 5, 4, 6, 3, 4, 4, 3, 4, 4, 3, 2, 7, 3, 3, 3, 5, 5, 3, 5, 3, 5, 2, 3, 4, 4, 5, 3, 4, 7, 3, 4, 3, 1, 5, 3, 3, 3, 4, 7, 5, 4, 3, 5, 3, 4, 4, 3, 4, 2, 4, 3, 5, 2, 2, 3

Offset: 0

Author

Hugo Pfoertner, Sep 16 2004

Keywords

• easy
• nonn

Comments

Number of nonzero bits in A098591(n).

The number a(n) is < 8 except for n=0. - Pierre CAMI, Jun 02 2009

For references to positions where a(n) = 7 and related explanation, see A100418. - Peter Munn, Sep 06 2023

Examples

			a(1)=7 because there are 7 primes in the interval (30,60): 31,37,41,43,47,53,59.
a(26)=3 because the interval of length 30 following 26*30=780 contains 3 primes: 787, 797 and 809.
		

Links

• Dennis Martin, Proofs Regarding Primorial Patterns [Cached copy, with permission of the author].
• Hugo Pfoertner, Patterns count table.

Crossrefs

Cf. A000040 (prime numbers), A098591 (packed representation of the primes mod 30), A100418, A185641.

Cf. A038822, A094892.

Programs

FORTRAN

! See links given in A098591.

PARI

a(n) = primepi(30*(n+1)) - primepi(30*n); \\ Michel Marcus, Apr 04 2020

Python

from sympy import primerange
def a(n): return len(list(primerange(n*30, (n+1)*30)))
print([a(n) for n in range(106)]) # Michael S. Branicky, Oct 07 2021

Extensions

Edited by N. J. A. Sloane, Jun 12 2009 at the suggestion of R. J. Mathar