

A065914


Number of primes in the interval [ 1/2 * q(n), 3/2 * q(n)  1 ] where q(n) is prime(n)#, the nth primorial.


2



1, 3, 8, 38, 294, 2922, 38949, 604764, 11635147, 287020007, 7721129740, 250811981714
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OFFSET

1,2


COMMENTS

Does lim q(n)/a(n+1) converge?


LINKS



FORMULA

a(n) = pi( 3*q(n)/2 1 )  pi( q(n)/2 1 ).


EXAMPLE

a(2) = 3 primes in [3,9], 93 = 6 = q(2) = 3*2. a(3) = 8 primes in [15,45], 4515 = 30 = q(3) = 5*6. a(4) = 38 primes in [105,315], 315105 = 210 = q(4) = 7*30.


PROG

(Python)
from __future__ import division
from sympy import primepi, primorial
pm = primorial(n)
return primepi(3*pm//21)primepi(pm//21) # Chai Wah Wu, Apr 28 2018
(PARI) q(n) = prod(k=1, n, prime(k)); \\ A002110
a(n) = my(nb=q(n)); primepi(3*nb/21)primepi(nb/21); \\ Michel Marcus, Aug 04 2021


CROSSREFS



KEYWORD

nonn,more


AUTHOR



EXTENSIONS



STATUS

approved



