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

1,2

Links

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

Formula

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

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 *)

Prog

(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

Crossrefs

Cf. A101947, A101983, A101984, A101985.

Sequence in context: A259981 A070705 A216326 * A215676 A130872 A087627

Adjacent sequences: A101906 A101907 A101908 * A101910 A101911 A101912

Keyword

easy,nonn

Author

Cino Hilliard, Jan 28 2005

Status

approved