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Search: id:A069922
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| A069922 |
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Number of primes p such that n^n<=p<=n^n+n^2. |
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+0
1
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| 1, 2, 2, 4, 1, 5, 4, 1, 2, 5, 1, 4, 4, 9, 7, 6, 2, 4, 7, 9, 7, 3, 7, 10, 10, 6, 12, 6, 10, 7, 8, 10, 7, 9, 13, 13, 7, 10, 11, 11, 9, 13, 11, 10, 15, 10, 11, 10, 19, 14, 16, 11, 16, 21, 20, 12, 9, 15, 21, 12, 10, 16, 15, 22, 19
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Question: for any n>0 is there at least one prime p such that n^n<=p<=n^n+n^2? In this case, that would be stronger than the Schinzel conjecture : "for m >1 there's at least one prime p such that m<=p<=m+ln(m)^2" since n^2<ln(n^n)^2=n^2*ln(n)^2.
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PROGRAM
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(PARI) for(n=1, 65, print1(sum(i=n^n, n^n+n^2, isprime(i)), ", "))
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CROSSREFS
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Sequence in context: A066202 A027420 A116588 this_sequence A072211 A070306 A014665
Adjacent sequences: A069919 A069920 A069921 this_sequence A069923 A069924 A069925
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KEYWORD
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easy,nonn
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr), May 05 2002
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