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

Author

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

Keywords

• cons
• nonn

Examples

			0.83274617727686715064641751940811553516243153102632810163149819758458\ 1351446095842290202600344430630467860292319092706478030883524064025...
		

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.

Crossrefs

Cf. A001620, A002162, A158468.

Programs

Mathematica

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

PARI

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

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