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A065914
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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.
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1
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1, 3, 8, 38, 294, 2922, 38949, 604764, 11635147, 287020007, 7721129740, 250811981714
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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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]
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FORMULA
| a(n) = pi( 3*q(n)/2 -1 ) - pi( q(n)/2 -1 ).
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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.
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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), ", "))
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CROSSREFS
| q(n) = A002110(n), pi(n) = A000720(n).
Sequence in context: A099030 A190658 A106558 * A180368 A108262 A034892
Adjacent sequences: A065911 A065912 A065913 * A065915 A065916 A065917
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KEYWORD
| nonn,more
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AUTHOR
| Frank Ellermann (hmdmhdfmhdjmzdtjmzdtzktdkztdjz(AT)gmail.com), Dec 07 2001
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EXTENSIONS
| Corrected by Jason Earls (zevi_35711(AT)yahoo.com), Dec 19 2001
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