A070046 Number of primes between prime(n) and 2*prime(n) exclusive.

1, 1, 1, 2, 3, 3, 4, 4, 5, 6, 7, 9, 9, 9, 9, 11, 13, 12, 13, 14, 13, 15, 15, 16, 19, 20, 19, 19, 18, 18, 23, 23, 25, 25, 27, 26, 28, 28, 28, 28, 30, 30, 32, 32, 32, 32, 35, 38, 38, 38, 39, 39, 39, 41, 42, 43, 42, 42, 42, 42, 42, 44, 49, 50, 49, 49, 54, 54, 56, 55, 55, 55, 57, 58

Offset

1,4

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Bertrand's Postulate

Formula

a(n) = primepi(2*prime(n))-n. - Charles R Greathouse IV, Aug 28 2014

a(n) = A060715(A000040(n)).

Example

a(1)=1 because between p=2 and 4 there is exactly one prime, 3.
a(10)=6 since six consecutive primes (31,37,41,43,47,53) are located between p(10) = 29 and 58.

Maple

N:= 1000: # to get a(n) for n <= pi(N)
Primes:=select(isprime, [$1..N]):
seq(numtheory:-pi(2*Primes[n])-n, n=1..nops(Primes)); # Robert Israel, Aug 28 2014

Mathematica

pp[n_]:=Module[{pr=Prime[n]}, PrimePi[2pr]-n]; Array[pp, 80] (* Harvey P. Dale, Mar 30 2015; edited by Zak Seidov, Oct 18 2022  *)

Prog

(PARI) forprime(p=2, 5000, n=0; for(q=p+1, 2*p-1, if(isprime(q), n++)); print1(n, ", ")) \\Harry J. Smith, Dec 13 2007, improved by Colin Barker, Aug 28 2014
(PARI) a(n)=primepi(2*prime(n))-n \\ Charles R Greathouse IV, Aug 28 2014

Crossrefs

Cf. A060715, A077463, A246514.

Sequence in context: A076895 A282029 A029086 * A130120 A204892 A164512

Adjacent sequences: A070043 A070044 A070045 * A070047 A070048 A070049

Keyword

easy,nonn

Author

Enoch Haga, May 05 2002

Extensions

Edited by N. J. A. Sloane, May 15 2008 at the suggestion of R. J. Mathar

Status

approved