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

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, 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, 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

Offset: 0

Author

Alexander Adamchuk, Aug 22 2006

Keywords

• cons
• nonn

Comments

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, ...

Examples

			C = 0.2132817487007856982556274813698484360277279725322464100714222201238395676003\
726900563712201186188234415559844581411471306301650311286030077813464608267160\
801494597797561591251174806253914566160177882...
		

Crossrefs

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