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%I #20 Jun 06 2021 19:21:03
%S 3,4,5,6,9,10,13,16,17,18,37,43,58,121,124,126,137,203,247,283,285,
%T 286,289,317,424,508,751,790,937,958,1066,1097,1151,1166,1194,1199,
%U 1235,1414,1418,1460,1498,1573,2090,2122,2691,2718,3030,3426,3600,3653,3737
%N Numbers k such that A058313(k) is prime.
%C A058313(k) = Numerator of Sum_{j=1..k} (-1)^(j+1)/j.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HarmonicNumber.html">Harmonic Number</a>
%t Do[ f=Numerator[ Sum[ (-1)^(k+1)*1/k, {k,1,n} ] ]; If[ PrimeQ[f], Print[ {n,f} ] ], {n,1,317} ]
%o (PARI) isok(n) = isprime(numerator(sum(k=1, n, (-1)^(k+1)/k))); \\ _Michel Marcus_, Mar 14 2019
%Y Cf. A058313, A119682, A120296, A136675, A136676, A136677.
%Y Cf. A001008, A007406, A007408, A007410, A099828, A103345.
%Y Cf. A136682, A136683, A136684, A136685, A136686.
%K nonn
%O 1,1
%A _Alexander Adamchuk_, Jan 16 2008
%E a(25)-a(30) from _James R. Buddenhagen_, Sep 22 2015
%E a(31)-a(51) from _Amiram Eldar_, Mar 14 2019