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.

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

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