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Search: id:A092101
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| 5, 13, 17, 23, 41, 67, 73, 79, 107, 113, 139, 149, 157, 179, 191, 193, 223, 239, 241, 251, 263, 277, 281, 293, 307, 311, 317, 331, 337, 349, 431, 443, 449, 461, 467, 479, 487, 491, 499, 503, 541, 547
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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For p = prime(n), Boyd defines Jp to be the set of numbers k such that p divides A001008(k), the numerator of the harmonic number H(k). For harmonic primes, Jp contains only the three numbers p-1, (p-1)p and (p-1)(p+1). It has been conjectured that there are an infinite number of these primes and that their density in the primes is 1/e.
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REFERENCES
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David W. Boyd, A p-adic study of the partial sums of the harmonic series, Experimental Math., Vol. 3 (1994), No. 4, 287-302.
A. Eswarathasan and E. Levine, p-integral harmonic sums, Discrete Math. 91 (1991), 249-257.
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LINKS
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David W. Boyd, A p-adic study of the partial sums of the harmonic series, Experimental Math., Vol. 3 (1994), No. 4, 287-302.
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CROSSREFS
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Cf. A092102 (non-harmonic primes), A092103 (size of Jp).
Sequence in context: A014539 A074278 A087895 this_sequence A105596 A037046 A126887
Adjacent sequences: A092098 A092099 A092100 this_sequence A092102 A092103 A092104
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KEYWORD
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nonn
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AUTHOR
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T. D. Noe (noe(AT)sspectra.com), Feb 20 2004
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