The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 60th year, we have over 367,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A065914 Number of primes in the interval [ 1/2 * q(n), 3/2 * q(n) - 1 ] where q(n) is prime(n)#, the n-th primorial. 2
 1, 3, 8, 38, 294, 2922, 38949, 604764, 11635147, 287020007, 7721129740, 250811981714 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Does lim q(n)/a(n+1) converge? The Prime Number Theorem implies that the limit is 1. [Charles R Greathouse IV, Dec 08 2011] LINKS Table of n, a(n) for n=1..12. FORMULA a(n) = pi( 3*q(n)/2 -1 ) - pi( q(n)/2 -1 ). EXAMPLE a(2) = 3 primes in [3,9], 9-3 = 6 = q(2) = 3*2. a(3) = 8 primes in [15,45], 45-15 = 30 = q(3) = 5*6. a(4) = 38 primes in [105,315], 315-105 = 210 = q(4) = 7*30. PROG (Python) from __future__ import division from sympy import primepi, primorial def A065914(n): pm = primorial(n) return primepi(3*pm//2-1)-primepi(pm//2-1) # 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/2-1)-primepi(nb/2-1); \\ Michel Marcus, Aug 04 2021 CROSSREFS q(n) = A002110(n), pi(n) = A000720(n). Sequence in context: A190658 A366629 A106558 * A288759 A180368 A108262 Adjacent sequences: A065911 A065912 A065913 * A065915 A065916 A065917 KEYWORD nonn,more AUTHOR Frank Ellermann, Dec 07 2001 EXTENSIONS Corrected by Jason Earls, Dec 19 2001 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 2 15:57 EST 2023. Contains 367524 sequences. (Running on oeis4.)