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A091812 Decimal expansion of sum(k>0,(-1)^k*log(k)/k). 3
1, 5, 9, 8, 6, 8, 9, 0, 3, 7, 4, 2, 4, 3, 0, 9, 7, 1, 7, 5, 6, 9, 4, 7, 8, 7, 0, 3, 2, 4, 9, 1, 6, 5, 7, 0, 4, 9, 6, 2, 2, 2, 0, 2, 3, 7, 5, 6, 4, 5, 8, 7, 4, 2, 6, 7, 0, 8, 2, 4, 5, 2, 9, 6, 3, 9, 6, 5, 7, 0, 0, 2, 1, 8, 4, 0, 2, 9, 0, 0, 4, 6, 5, 9, 5, 5, 5, 0, 3, 4, 0, 3, 2, 0, 4, 6, 1, 8, 8, 2, 9, 4, 6, 3 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Equal to the derivative eta'(1) of the Dirichlet eta function eta(s) = sum(k>0, (-1)^(k-1)/k^s) = (1 - 2^(1-s))*zeta(s) at s = 1. - Jonathan Sondow, Dec 28 2011.

LINKS

Table of n, a(n) for n=0..103.

FORMULA

Decimal expansion of sum(k>0, (-1)^k*log(k)/k) = gamma*log(2)-log(2)^2/2.

EXAMPLE

0.15986890374243097175694787032491657049622202375645874267082452963965...

PROG

(PARI) Euler*log(2)-log(2)^2/2 \\ Charles R Greathouse IV, Mar 28, 2012

CROSSREFS

Cf. A265162.

Sequence in context: A249385 A247747 A217249 * A112678 A021171 A011493

Adjacent sequences:  A091809 A091810 A091811 * A091813 A091814 A091815

KEYWORD

cons,nonn

AUTHOR

Benoit Cloitre, Mar 07 2004

STATUS

approved

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Last modified July 20 14:50 EDT 2017. Contains 289625 sequences.