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A122147 Decimal expansion of Sum[ (-1)^(k+1) * 1/p(k)^p(k) ], where p(k) = Prime[k].

%I A122147 #4 Mar 31 2012 13:20:28
%S A122147 2,1,3,2,8,1,7,4,8,7,0,0,7,8,5,6,9,8,2,5,5,6,2,7,4,8,1,3,6,9,8,4,8,4,
%T A122147 3,6,0,2,7,7,2,7,9,7,2,5,3,2,2,4,6,4,1,0,0,7,1,4,2,2,2,2,0,1,2,3,8,3,
%U A122147 9,5,6,7,6,0,0,3,7,2,6,9,0,0,5,6,3,7,1,2,2,0,1,1,8,6,1,8,8,2,3,4,4,1,5,5,5
%N A122147 Decimal expansion of Sum[ (-1)^(k+1) * 1/p(k)^p(k) ], where p(k) = Prime[k].
%C A122147 C = Sum[ (-1)^(k+1) * 1/Prime[k]^Prime[k], {k,1,Infinity} ] = 1/2^2 - 1/3^3 + 1/5^5 - 1/7^7 + 1/11^11 - 1/13^13 + ... Partial sums are A122148[n] / A076265[n] = Sum[ (-1)^(k+1) * 1/Prime[k]^Prime[k], {k,1,n} ] = 1/4, 23/108, 71983/337500, ...
%e A122147 C = 0.2132817487007856982556274813698484360277279725322464100714222201238395676003\
%e A122147 726900563712201186188234415559844581411471306301650311286030077813464608267160\
%e A122147 801494597797561591251174806253914566160177882...
%Y A122147 Cf. A051674, A122148, A076265, A094289, A117579, A076265, A000040.
%K A122147 cons,nonn
%O A122147 0,1
%A A122147 _Alexander Adamchuk_, Aug 22 2006