A075699 Number of primes in the interval (n,4n].

2, 3, 3, 4, 5, 6, 5, 7, 7, 8, 9, 10, 9, 10, 11, 12, 12, 13, 13, 14, 15, 15, 15, 15, 16, 18, 19, 20, 20, 20, 19, 20, 21, 21, 23, 23, 22, 24, 24, 25, 25, 26, 25, 26, 27, 28, 27, 28, 29, 31, 31, 31, 31, 31, 31, 32, 33, 34, 34, 35, 35, 35, 36, 36, 37, 38, 37, 39, 39, 40, 41, 41, 40

Offset: 1

Author

Zak Seidov, Oct 02 2002

Keywords

• nonn

Comments

Difference a(n+1) - a(n) = -1, 0, 1, 2, ... .

Examples

			a(4) = 4 because between 4 and 16 there are 4 primes: 5, 7, 11, 13.
a(7) = 5 because between 7 and 28 there are 5 primes: 11, 13, 17, 19, 23.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Madhuparna Das and Goutam Paul, Revisiting Generalized Bertand's Postulate and Prime Gaps, arXiv:1710.09891 [math.NT], 2017-2019.

Crossrefs

Cf. A000720, A074990, A108954.

Programs

Maple

A075699 := proc(n)
    numtheory[pi](4*n)-numtheory[pi](n) ;
end proc: # R. J. Mathar, Nov 03 2017

Mathematica

s=4; a[n_] := PrimePi[s*n]-PrimePi[n]

PARI

a(n) = primepi(4*n) - primepi(n); \\ Michel Marcus, Oct 02 2013

Formula

a(n) = A000720(4n) - A000720(n). - Michel Marcus, Oct 02 2013