A355923 Decimal expansion of Sum_{k>=2} (arctanh(1/k) - 1/k).

7, 6, 2, 1, 0, 7, 4, 4, 8, 1, 8, 4, 9, 4, 4, 8, 4, 6, 8, 4, 8, 7, 1, 8, 4, 9, 1, 8, 8, 5, 0, 9, 2, 8, 4, 9, 2, 0, 0, 9, 0, 5, 9, 6, 8, 7, 9, 9, 4, 8, 7, 7, 4, 1, 3, 3, 8, 9, 2, 7, 6, 0, 3, 6, 8, 4, 3, 5, 4, 6, 2, 2, 3, 7, 4, 8, 7, 9, 7, 1, 2, 6, 0, 1, 2, 1, 2, 7, 3, 2, 1, 0, 0, 4, 3, 9, 0, 6, 7, 1, 4, 3, 6, 7, 8

Offset

-1,1

Links

Table of n, a(n) for n=-1..103.

Michael Ian Shamos, Shamos's Catalog of the Real Numbers, 2011, pp. 126-127.

Formula

Equals Sum_{k>=1} (zeta(2*k+1)-1)/(2*k+1).

Equals 1 - gamma - log(2)/2, where gamma is Euler's constant (A001620).

Equals Sum_{k>=2} ((1/2)*log((k+1)/(k-1)) - 1/k).

Equals 2 * Integral_{x>=0} x * exp(-x) * log(x) * sin(x) dx.

Example

0.07621074481849448468487184918850928492009059687994877413...

Mathematica

RealDigits[1 - EulerGamma - Log[2]/2, 10, 100][[1]]

Crossrefs

Cf. A001620, A002162, A016655, A239097, A352619, A355922.

Sequence in context: A152861 A285165 A198925 * A260333 A138096 A258010

Adjacent sequences: A355920 A355921 A355922 * A355924 A355925 A355926

Keyword

nonn,cons

Author

Amiram Eldar, Jul 21 2022

Status

approved