A056903 Numbers n such that the numerator of the rational number 1 + 1/2 + 1/3 + ... + 1/n is a prime number.

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

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: A120057 A099422 A294913 * A229139 A293277 A331864

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