Search: id:A056903
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%I A056903
%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="b056903.txt">Table of n, a(n) for n = 1..97</
               a>
%H A056903 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               HarmonicNumber.html">Harmonic Number</a>
%H A056903 Eric Weisstein's World of Mathematics, <a href="http://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[ # ]]] &]
%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).
%Y A056903 Sequence in context: A104737 A120057 A099422 this_sequence A028770 A028800 
               A028841
%Y A056903 Adjacent sequences: A056900 A056901 A056902 this_sequence A056904 A056905 
               A056906
%K A056903 nonn
%O A056903 1,1
%A A056903 Jim Buddenhagen (jbuddenh(AT)gmail.com), Feb 23 2001
%E A056903 Terms from 201 to 492 computed by Jud McCranie (j.mccranie(AT)comcast.net).
%E A056903 More terms from Kamil Duszenko (kdusz(AT)wp.pl), Jun 22 2003
%E A056903 29 more terms from T. D. Noe (noe(AT)sspectra.com), Sep 15 2004
%E A056903 Further terms found by Eric Weisstein (eric(AT)weisstein.com), Mar 07 
               2005, Mar 29 2005, Nov 28 2005, Sep 23 2006

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