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Search: id:A056903
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| A056903 |
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Numbers n such that the numerator of the rational number 1 + 1/2 + 1/3 + ... + 1/n is a prime number. |
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+0
14
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| 2, 3, 5, 8, 9, 21, 26, 41, 56, 62, 69, 79, 89, 91, 122, 127, 143, 167, 201, 230, 247, 252, 290, 349, 376, 459, 489, 492, 516, 662, 687, 714, 771, 932, 944, 1061, 1281, 1352, 1489, 1730, 1969, 2012, 2116, 2457, 2663, 2955, 3083, 3130, 3204, 3359, 3494, 3572
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Related to partial sums of the harmonic series and to Wolstenholme's Theorem.
Some of the larger entries may only correspond to probable primes.
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LINKS
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Eric Weisstein, Table of n, a(n) for n = 1..97
Eric Weisstein's World of Mathematics, Harmonic Number
Eric Weisstein's World of Mathematics, Integer Sequence Primes
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EXAMPLE
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5 is in this sequence because 1+1/2+1/3+1/4+1/5 = 137/60 and 137 is prime.
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MATHEMATICA
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Select[Range[1000], PrimeQ[Numerator[HarmonicNumber[ # ]]] &]
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CROSSREFS
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Cf. A002387, A004080.
Cf. A001008 (numerator of the harmonic number H(n)), A067657 (primes that are the numerator of a harmonic number).
Sequence in context: A104737 A120057 A099422 this_sequence A028770 A028800 A028841
Adjacent sequences: A056900 A056901 A056902 this_sequence A056904 A056905 A056906
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KEYWORD
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nonn
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AUTHOR
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Jim Buddenhagen (jbuddenh(AT)gmail.com), Feb 23 2001
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EXTENSIONS
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Terms from 201 to 492 computed by Jud McCranie (j.mccranie(AT)comcast.net).
More terms from Kamil Duszenko (kdusz(AT)wp.pl), Jun 22 2003
29 more terms from T. D. Noe (noe(AT)sspectra.com), Sep 15 2004
Further terms found by Eric Weisstein (eric(AT)weisstein.com), Mar 07 2005, Mar 29 2005, Nov 28 2005, Sep 23 2006
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