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A307671 Decimal expansion of the alternating convergent series S = Sum_{k>=0} (-1)^k*f(k), where f(k) = harmonic(2^k) - k*log(2) - gamma, harmonic(m) is the Sum_{j=1..m} 1/j, and gamma is Euler-Mascheroni constant. 0
2, 7, 2, 3, 4, 3, 5, 8, 7, 7, 0, 7, 5, 9, 6, 7, 6, 4, 7, 8, 4, 0, 7, 0, 6, 7, 6, 9, 2, 3, 9, 5, 5, 5, 7, 8, 7, 4, 8, 2, 2, 5, 1, 0, 8, 0, 6, 4, 3, 9, 5, 8, 7, 1, 6, 4, 5, 3, 8, 9, 6, 2, 0, 4, 1, 2, 8, 3, 7, 5, 9, 7, 0, 0, 5, 7, 2, 9, 6, 5, 1, 1, 5, 0, 1, 2, 9, 8, 4, 6, 1, 7, 7, 3, 1, 3, 1, 7, 3, 9, 8, 0, 2, 7 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

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

EXAMPLE

0.272343587707596764784070676923955578748225108064395871645389620412837597...

MAPLE

evalf(Sum((-1)^k*(harmonic(2^k) - k*log(2) - gamma), k=0..infinity), 120); # Vaclav Kotesovec, Apr 30 2019

MATHEMATICA

digits = 104; s = NSum[(-1)^k*(HarmonicNumber[2^k] - k*Log[2] - EulerGamma), {k, 0, Infinity}, Method -> "AlternatingSigns", WorkingPrecision -> digits+10]; RealDigits[s, 10, digits][[1]] (* Jean-François Alcover, Apr 28 2019 *)

PROG

(PARI) default(realprecision, 120); sumalt(k=0, (-1)^k*(psi(2^k+1) - k*log(2))) \\ Vaclav Kotesovec, Apr 30 2019

CROSSREFS

Cf. A001620 (Euler-Mascheroni), A001008/A002805 (harmonic), A002162 (log(2)), A094640 (alternate Euler's constant), A256921 (a similar constant).

Sequence in context: A266390 A171685 A011048 * A011401 A265647 A078202

Adjacent sequences:  A307668 A307669 A307670 * A307672 A307673 A307674

KEYWORD

cons,nonn

AUTHOR

Luis H. Gallardo, Apr 20 2019

STATUS

approved

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Last modified December 6 18:16 EST 2021. Contains 349567 sequences. (Running on oeis4.)