A074990 Number of primes in the interval (n,3n].

2, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 6, 6, 7, 8, 9, 8, 9, 8, 9, 10, 10, 10, 11, 12, 12, 13, 14, 13, 14, 13, 13, 14, 15, 16, 17, 17, 18, 18, 18, 17, 17, 17, 18, 18, 19, 19, 19, 19, 20, 21, 21, 21, 21, 22, 23, 23, 24, 23, 24, 24, 24, 24, 25, 26, 27, 27, 27, 27, 27, 27, 27, 26, 26, 27, 28

Offset: 1

Author

Zak Seidov, Oct 02 2002

Keywords

• nonn

Comments

Differences a(n+1)-a(n) are 0, 1 or -1.

Examples

			a(4) = 3 because between 4 and 12 there are 3 primes: 5, 7, 11; a(7) = 4 because between 7 and 21 there are 4 primes: 11, 13, 17, 19.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000
• 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.

Crossrefs

Cf. A000040, A000720, A010051, A108954, A075699.

Programs

Maple

A074990 := proc(n)
    numtheory[pi](3*n)-numtheory[pi](n) ;
end proc: # R. J. Mathar, Nov 03 2017

Mathematica

s=3; a[n_] := PrimePi[s*n]-PrimePi[n]

Formula

a(n) = A000720(3n) - A000720(n).

a(n) = Sum_{j=n+1..3*n} A010051(j).