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

1,1

Comments

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

Links

Table of n, a(n) for n=1..73.

M. Das, G. Paul, Generalization of Bertrand's Postulate and Upper Bounds on the Number of Primes in Certain Intervals, arXiv:1710.09891 [math.NT], 2017-2019.

Formula

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

Example

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.

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]

Prog

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

Crossrefs

Cf. A108954, A074990.

Sequence in context: A103827 A094182 A300587 * A112330 A332682 A304183

Adjacent sequences: A075696 A075697 A075698 * A075700 A075701 A075702

Keyword

nonn

Author

Zak Seidov, Oct 02 2002

Status

approved