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%I #10 Feb 12 2019 08:42:47
%S 3,2,2,3,2,19,2,146,87,3,16,3,2,249,15,87,2,699,2
%N Smallest number k such that the numerator of alternating generalized harmonic number H'(k,n) = Sum[ (-1)^(i+1) * 1/i^n, {i,1,k} ] is a prime.
%C a(n) = 2 for n in A000043.
%C a(n) = 3 for n in {1,4,10,12,24,27,39,...}.
%C a(n) = 5 for n in {26,76,132,205,238,...}.
%C a(n) = 9 for n in {100,200,...}.
%C a(n) = 15 for n in {15,33,65,...}.
%C a(21) = 18. a(22) = 13. a(41) = 6. a(72) = 11. a(173) = 8.
%C a(20) > 2100 - _Max Alekseyev_, Jul 07 2009
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HarmonicNumber.html">Harmonic Number</a>
%Y Cf. A058313, A119682, A120296, A001008, A000043.
%K hard,more,nonn
%O 1,1
%A _Alexander Adamchuk_, Dec 28 2006, Jan 31 2007
%E More terms from _Max Alekseyev_, Jul 07 2009
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