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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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13
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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
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history;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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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
J. Sondow and E. W. Weisstein, MathWorld: 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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PROG
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(Perl) use ntheory ":all"; for (1..1000) { say if is_prime((harmfrac($_))[0]); } # Dana Jacobsen, Feb 05 2016
(PARI) isok(n) = isprime(numerator(sum(k=1, n, 1/k))); \\ Michel Marcus, Feb 05 2016
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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: A120057 A099422 A294913 * A229139 A293277 A331864
Adjacent sequences: A056900 A056901 A056902 * A056904 A056905 A056906
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KEYWORD
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nonn
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AUTHOR
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James R. Buddenhagen, Feb 23 2001
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EXTENSIONS
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Terms from 201 to 492 computed by Jud McCranie.
More terms from Kamil Duszenko (kdusz(AT)wp.pl), Jun 22 2003
29 more terms from T. D. Noe, Sep 15 2004
Further terms found by Eric W. Weisstein, Mar 07 2005, Mar 29 2005, Nov 28 2005, Sep 23 2006
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STATUS
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approved
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