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Search: id:A135714
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| A135714 |
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Number of primes of the form p(n)#/p(k) - 1, where 1 <= k <= n. |
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+0
3
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| 0, 1, 1, 2, 2, 4, 2, 3, 4, 1, 0, 3, 3, 3, 3, 5, 2, 0, 3, 3, 5, 2, 2, 1, 5, 4, 2, 1, 2, 0, 0, 1, 1, 2, 3, 1, 2, 3, 1, 2, 1, 3, 0, 3, 4, 0, 4, 1, 0, 1, 3, 0, 2, 2, 5, 1, 2, 1, 5, 1, 1, 2, 1, 1, 3, 6, 3, 2, 4, 4, 0, 1, 2, 2, 4, 1, 4, 2, 1, 1, 2, 1, 2, 2, 2, 2, 2, 4, 2, 2, 0, 4, 3, 2, 2, 4, 1, 0, 0, 2, 2, 3, 4, 4, 3
(list; graph; listen)
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OFFSET
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1,4
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COMMENT
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p(k) is k-th prime; p(n)# is n-th primorial, A002110(n). For the larger n, these are only counts of highly probable primes. Of the first 500 terms, the maximum occurs twice, a(366)=a(432)=7; the mode is 2, occurring 142 times.
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LINKS
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Rick Shepherd, Table of n, a(n) for n = 1..500
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EXAMPLE
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a(6)=4 because p(6)#=A002110(6)=30030 and 30030/3-1=10009, 30030/7-1=4289, 30030/11-1=2729, and 30030/13-1=2309 are all prime and there are no other primes of this form.
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PROGRAM
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(PARI) a(n)= p=prod(k=1, n, prime(k)); sum(k=1, n, isprime(p/prime(k)-1))
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CROSSREFS
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Cf. A135715, A135716, A002110.
Sequence in context: A092607 A057939 A061338 this_sequence A103274 A046820 A043262
Adjacent sequences: A135711 A135712 A135713 this_sequence A135715 A135716 A135717
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KEYWORD
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nonn
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AUTHOR
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Rick L. Shepherd (rshepherd2(AT)hotmail.com), Nov 28 2007
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