A100668 Decimal expansion of the base-2 analog of the Euler-Mascheroni constant.

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

Offset

0,1

Links

Alois P. Heinz, Table of n, a(n) for n = 0..10000

Hartosh Singh Bal and Gaurav Bhatnagar, Prime number conjectures from the Shapiro class structure, arXiv:1903.09619 [math.NT], 2019.

Eric Weisstein's World of Mathematics, Euler-Mascheroni Constant.

Eric Weisstein's World of Mathematics, Harmonic Number (with contribution from Jonathan Sondow).

Eric Weisstein's World of Mathematics, Lg.

Formula

EulerGamma/log(2) = A001620/A002162.

Equals Integral_{x=-infinity..infinity} x*2^(-x)*log(2)*exp(-2^(-x)) dx. - Alois P. Heinz, Nov 09 2016

Example

0.83274617727686715064641751940811553516243153102632810163149819758458\ 1351446095842290202600344430630467860292319092706478030883524064025...

Mathematica

RealDigits[Limit[Sum[D[Log[2, x], x] /. x -> k, {k, 1, n}] - Log[2, n], n -> Infinity], 10, 135][[1]]

Prog

(PARI) Euler/log(2) \\ Michel Marcus, Jun 02 2020

Crossrefs

Cf. A001620, A002162, A158468.

Sequence in context: A063568 A302138 A198494 * A194159 A154158 A100863

Adjacent sequences: A100665 A100666 A100667 * A100669 A100670 A100671

Keyword

cons,nonn

Author

Joseph Biberstine (jrbibers(AT)indiana.edu), Dec 05 2004

Status

approved