login
A100668
Decimal expansion of the base-2 analog of the Euler-Mascheroni constant.
4
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
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
KEYWORD
cons,nonn
AUTHOR
Joseph Biberstine (jrbibers(AT)indiana.edu), Dec 05 2004
STATUS
approved