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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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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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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. A001008 (numerator of the harmonic number H(n)), A067657 (primes that are the numerator of a harmonic number).
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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More terms from Kamil Duszenko (kdusz(AT)wp.pl), Jun 22 2003
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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