A101909 Number of primes between 2n and 4n.

1, 2, 2, 2, 4, 4, 3, 5, 4, 4, 6, 6, 6, 7, 7, 7, 8, 9, 9, 10, 10, 9, 10, 9, 10, 12, 12, 13, 14, 13, 12, 13, 14, 13, 15, 14, 13, 15, 15, 15, 16, 16, 16, 17, 17, 18, 18, 19, 19, 21, 20, 19, 20, 19, 18, 19, 19, 20, 21, 22, 23, 23, 24, 23, 24, 24, 24, 26, 25, 25, 27, 27, 27, 28, 27, 26

Offset: 1

Author

Cino Hilliard, Jan 28 2005

Keywords

• easy
• nonn

Links

• T. D. Noe and Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A101947, A101983, A101984, A101985.

Programs

Maple

A101909 := proc(n::integer)
    numtheory[pi](4*n)-numtheory[pi](2*n) ;
end proc:
seq(A101909(n),n=1..100) ; # R. J. Mathar, Oct 02 2019

Mathematica

f[n_] := PrimePi[4n] - PrimePi[2n]; Table[ f[n], {n, 76}] (* Robert G. Wilson v, Feb 10 2005 *)

PARI

bet2n4n(n) = { local(c,x,y); forstep(x=2,n,2, c=0; forprime(y=x+1,x+x-1, c++; ); print1(c",") ) }

PARI

s=0;vector(100,n,s+=isprime(4*n-1)+isprime(4*n-3)-isprime(2*n-1)) \\ Charles R Greathouse IV, Mar 12 2012

Formula

a(n) = A099802(2*n)-A099802(n). - R. J. Mathar, Oct 02 2019