This site is supported by donations to The OEIS Foundation.

 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 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 (PARI) pi(x)=c=0; forprime(p=2, x, c++); c q(n) = prod(k=1, n, prime(k)) a(n) = pi(3*q(n)/2-1)-pi(q(n)/2-1) for(n=1, 11, print1(a(n), ", ")) (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 CROSSREFS q(n) = A002110(n), pi(n) = A000720(n). Sequence in context: A264657 A190658 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 | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 15 20:11 EDT 2019. Contains 327086 sequences. (Running on oeis4.)