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%I #35 Jan 30 2021 04:07:09
%S 5,9,11,13,17,20,21,23,25,29,32,33,35,37,38,39,41,43,44,45,47,49,50,
%T 51,53,54,55,56,57,59,61,62,64,65,67,68,69,71,73,75,77,79,81,83,84,85,
%U 86,89,90,91,92,93,94,95,97,98,101,104,105,107,109,110,111,113
%N Numbers k such that d(k) = d(k+1), where d(k) = A058312(k) is the denominator of the k-th alternating harmonic number.
%C The asymptotic density of this sequence is 1 (Wu and Chen, 2019).
%H Amiram Eldar, <a href="/A337920/b337920.txt">Table of n, a(n) for n = 1..10000</a>
%H Bing-Ling Wu and Yong-Gao Chen, <a href="https://doi.org/10.1016/j.jnt.2018.11.026">On the denominators of harmonic numbers, II</a>, Journal of Number Theory, Vol. 200 (2019), pp. 397-406.
%e 5 is a term since A058312(5) = A058312(6) = 60.
%t d[n_] := Denominator @ Sum[(-1)^(k + 1)/k, {k, 1, n}]; Position[Partition[d[Range[120]], 2, 1], {x_, x_}] // Flatten
%Y Cf. A058312, A065454 (analogous with denominators of harmonic numbers).
%K nonn
%O 1,1
%A _Amiram Eldar_, Jan 29 2021
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