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

Author

James R. Buddenhagen, Feb 23 2001

Keywords

• nonn

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.

Examples

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

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

Crossrefs

Cf. A002387, A004080.

Cf. A001008 (numerator of the harmonic number H(n)), A067657 (primes that are the numerator of a harmonic number).

Programs

Mathematica

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

PARI

isok(n) = isprime(numerator(sum(k=1, n, 1/k))); \\ Michel Marcus, Feb 05 2016

Perl

use ntheory ":all"; for (1..1000) { say if is_prime((harmfrac($))[0]); } # _Dana Jacobsen, Feb 05 2016

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