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Search: id:A065914
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| A065914 |
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Primes in interval [ q(n)/2, q(n)/2+q(n)-1 ] for primorial q(n). |
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+0
2
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| 1, 3, 8, 38, 294, 2922, 38949, 604764, 11635147, 287020007, 7721129740, 250811981714
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Does lim q(n)/a(n+1) converge?
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FORMULA
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a(n) = pi( 3*q(n)/2 -1 ) - pi( q(n)/2 -1 ).
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EXAMPLE
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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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PROGRAM
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(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
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q(n) = A002110(n), pi(n) = A000720(n).
Sequence in context: A089066 A099030 A106558 this_sequence A108262 A034892 A072687
Adjacent sequences: A065911 A065912 A065913 this_sequence A065915 A065916 A065917
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KEYWORD
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nonn,more
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AUTHOR
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frank.ellermann(AT)t-online.de, Dec 07 2001
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EXTENSIONS
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Corrected by Jason Earls (zevi_35711(AT)yahoo.com), Dec 19 2001
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