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%I #41 May 10 2020 08:37:57
%S 5,7,11,5,13,7,17,7,37,19,29,119,47,41,23,5,29,31,37,11,37,41,43,13,7,
%T 13,71,13,49,13,7,47,7,7,53,79,59,61,5,97,71,103,67,71,17,73,61,139,
%U 17,17,79,19,19,19,19,83,151,89,29,97,263,29,101,103,223,107,109,271,37,23,113,359
%N a(n) = A120301(A123944(n))/A058313(A123944(n)).
%C The ratio A120301(n)/A058313(n) = 1 for most n.
%C a(n) is prime for most n.
%C The first composite ratio a(12) = 119 = 7*17 corresponds to A123944(12) = 238.
%C The next two composite ratios a(29) = a(76) = 49 = 7^2 correspond to A123944(29) = 1470 and A123944(76) = 10290. [Edited by _Petros Hadjicostas_, May 09 2020]
%t f = 0; Do[f = f + (-1)^(n + 1) * 1/n; g = Abs[(2(-1)^n * n + (-1)^n - 1)/4] * f; rfg = Numerator[g]/Numerator[f]; If[(rfg == 1) == False, Print[rfg]], {n, 1500}]
%o (PARI) lista(nn) = {for (n=1, nn, my(sn = sum(k=1, n, (-1)^(k+1)/k)); if ((s=numerator(sn)) != (ss=abs(numerator((-1/4) * (2*(-1)^n*n + (-1)^n - 1) * sn))), print1(ss/s, ", ")););} \\ _Michel Marcus_, May 10 2020
%Y Cf. A058313, A120301, A123944.
%K nonn
%O 1,1
%A _Alexander Adamchuk_, Nov 02 2009
%E a(32)-a(46) from _Petros Hadjicostas_, May 09 2020, using _Michel Marcus_'s program and the data from A123944
%E a(47)-a(72) from _Petros Hadjicostas_, May 09 2020, using the Mathematica program
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