A122147 - OEIS

%I #4 Mar 31 2012 13:20:28

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

%C 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 C = 0.2132817487007856982556274813698484360277279725322464100714222201238395676003\

%e 726900563712201186188234415559844581411471306301650311286030077813464608267160\

%e 801494597797561591251174806253914566160177882...

%Y Cf. A051674, A122148, A076265, A094289, A117579, A076265, A000040.

%K cons,nonn

%O 0,1

%A _Alexander Adamchuk_, Aug 22 2006