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%I #6 Jan 16 2013 09:09:26
%S 5,11,2,79,331,479,5297,70061,69203,8960447,45083347,1031626241,
%T 15484789693,15537907043,64166447971,3979714828967,3988907823167,
%U 27918983997629,598858179567591121853,31710728461561839214229
%N Primes in A125683(n) = numerator[ Sum[ (-1)^(k+1) * 1/(k(k+1)), {k,1,n} ].
%C Corresponding numbers n such that A125683(n) is prime are listed in A125684(n) = {3,4,5,6,7,8,10,13,14,18,21,22,26,27,28,32,33,35,51,54,58,67,76,89,100,...}.
%H Vincenzo Librandi, <a href="/A125685/b125685.txt">Table of n, a(n) for n = 1..65</a>
%F a(n) = A125683[ A125684(n) ].
%e A125683(n) begins {1,1,5,11,2,79,331,479,493,5297,2701,69071,70061,...}.
%e Thus a(1) = 5 because A125683(3) = 5 is prime but A125683(k) is not prime for k<3.
%e a(2)-a(6) = {11,2,79,331,479} because A125683(k) is prime for 3<k<9.
%t Select[Table[Numerator[Sum[(-1)^(k+1)*1/(k(k+1)), {k, 1, n}]], {n, 1, 100}], PrimeQ]
%Y Cf. A125683, A125684.
%K nonn
%O 1,1
%A _Alexander Adamchuk_, Nov 30 2006
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