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A070046 Number of primes between prime(n) and 2*prime(n) exclusive. 6
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 (list; graph; refs; listen; history; text; internal format)
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]-PrimePi[pr]]; Array[pp, 80] (* Harvey P. Dale, Mar 30 2015 *)

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

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Last modified September 27 19:34 EDT 2021. Contains 347694 sequences. (Running on oeis4.)