

A056903


Numbers n such that the numerator of the rational number 1 + 1/2 + 1/3 + ... + 1/n is a prime number.


14



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

1,1


COMMENTS

Related to partial sums of the harmonic series and to Wolstenholme's Theorem.
Some of the larger entries may only correspond to probable primes.


LINKS

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


EXAMPLE

5 is in this sequence because 1+1/2+1/3+1/4+1/5 = 137/60 and 137 is prime.


MATHEMATICA

Select[Range[1000], PrimeQ[Numerator[HarmonicNumber[ # ]]] &]


PROG

(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


CROSSREFS

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: A278334 A120057 A099422 * A229139 A272669 A028770
Adjacent sequences: A056900 A056901 A056902 * A056904 A056905 A056906


KEYWORD

nonn


AUTHOR

James R. Buddenhagen, Feb 23 2001


EXTENSIONS

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


STATUS

approved



