login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

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.
0

%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