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A122147

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

#4 by Russ Cox at Sat Mar 31 13:20:28 EDT 2012

AUTHOR

_Alexander Adamchuk (alex(AT)kolmogorov.com), _, Aug 22 2006

Discussion

Sat Mar 31

13:20

OEIS Server: https://oeis.org/edit/global/879

#3 by N. J. A. Sloane at Fri Jan 09 03:00:00 EST 2009

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] / A122149A076265[n] = Sum[ (-1)^(k+1) * 1/Prime[k]^Prime[k], {k,1,n} ] = 1/4, 23/108, 71983/337500, ...

CROSSREFS

Cf. A051674, A122148, A122149, A076265, A094289, A117579, A076265, A000040.

KEYWORD

cons,nonn,new

#2 by N. J. A. Sloane at Sat Nov 10 03:00:00 EST 2007

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] / A122149[n] = Sum[ (-1)^(k+1) * 1/Prime[k]^Prime[k] , , {k,1,n} ] = 1/4, 23/108, 71983/337500, ...

KEYWORD

cons,nonn,new

#1 by N. J. A. Sloane at Fri Sep 29 03:00:00 EDT 2006

NAME

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

DATA

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

0,1

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] / A122149[n] = Sum[ (-1)^(k+1) * 1/Prime[k]^Prime[k] , {k,1,n} ] = 1/4, 23/108, 71983/337500, ...

EXAMPLE

C = 0.2132817487007856982556274813698484360277279725322464100714222201238395676003\

726900563712201186188234415559844581411471306301650311286030077813464608267160\

801494597797561591251174806253914566160177882...

CROSSREFS

Cf. A051674, A122148, A122149, A094289, A117579, A076265, A000040.

KEYWORD

cons,nonn

AUTHOR

Alexander Adamchuk (alex(AT)kolmogorov.com), Aug 22 2006

STATUS

approved