cp's OEIS Frontend

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

%I A056903 #32 Feb 16 2025 08:32:43
%S A056903 2,3,5,8,9,21,26,41,56,62,69,79,89,91,122,127,143,167,201,230,247,252,
%T A056903 290,349,376,459,489,492,516,662,687,714,771,932,944,1061,1281,1352,
%U A056903 1489,1730,1969,2012,2116,2457,2663,2955,3083,3130,3204,3359,3494,3572
%N A056903 Numbers n such that the numerator of the rational number 1 + 1/2 + 1/3 + ... + 1/n is a prime number.
%C A056903 Related to partial sums of the harmonic series and to Wolstenholme's Theorem.
%C A056903 Some of the larger entries may only correspond to probable primes.
%H A056903 Eric Weisstein, <a href="/A056903/b056903.txt">Table of n, a(n) for n = 1..97</a>
%H A056903 J. Sondow and E. W. Weisstein, <a href="https://mathworld.wolfram.com/HarmonicNumber.html">MathWorld: Harmonic Number</a>
%H A056903 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/IntegerSequencePrimes.html">Integer Sequence Primes</a>
%e A056903 5 is in this sequence because 1+1/2+1/3+1/4+1/5 = 137/60 and 137 is prime.
%t A056903 Select[Range[1000], PrimeQ[Numerator[HarmonicNumber[ # ]]] &]
%o A056903 (Perl) use ntheory ":all"; for (1..1000) { say if is_prime((harmfrac($_))[0]); } # _Dana Jacobsen_, Feb 05 2016
%o A056903 (PARI) isok(n) = isprime(numerator(sum(k=1, n, 1/k))); \\ _Michel Marcus_, Feb 05 2016
%Y A056903 Cf. A002387, A004080.
%Y A056903 Cf. A001008 (numerator of the harmonic number H(n)), A067657 (primes that are the numerator of a harmonic number).
%K A056903 nonn
%O A056903 1,1
%A A056903 _James R. Buddenhagen_, Feb 23 2001
%E A056903 Terms from 201 to 492 computed by _Jud McCranie_.
%E A056903 More terms from Kamil Duszenko (kdusz(AT)wp.pl), Jun 22 2003
%E A056903 29 more terms from _T. D. Noe_, Sep 15 2004
%E A056903 Further terms found by _Eric W. Weisstein_, Mar 07 2005, Mar 29 2005, Nov 28 2005, Sep 23 2006