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%I #31 Jun 02 2020 05:05:57
%S 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,
%T 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,
%U 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
%N Decimal expansion of the base-2 analog of the Euler-Mascheroni constant.
%H Alois P. Heinz, <a href="/A100668/b100668.txt">Table of n, a(n) for n = 0..10000</a>
%H Hartosh Singh Bal and Gaurav Bhatnagar, <a href="https://arxiv.org/abs/1903.09619">Prime number conjectures from the Shapiro class structure</a>, arXiv:1903.09619 [math.NT], 2019.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Euler-MascheroniConstant.html">Euler-Mascheroni Constant</a>.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HarmonicNumber.html">Harmonic Number</a> (with contribution from Jonathan Sondow).
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Lg.html">Lg</a>.
%F EulerGamma/log(2) = A001620/A002162.
%F Equals Integral_{x=-infinity..infinity} x*2^(-x)*log(2)*exp(-2^(-x)) dx. - _Alois P. Heinz_, Nov 09 2016
%e 0.83274617727686715064641751940811553516243153102632810163149819758458\ 1351446095842290202600344430630467860292319092706478030883524064025...
%t RealDigits[Limit[Sum[D[Log[2, x], x] /. x -> k, {k, 1, n}] - Log[2, n], n -> Infinity], 10, 135][[1]]
%o (PARI) Euler/log(2) \\ _Michel Marcus_, Jun 02 2020
%Y Cf. A001620, A002162, A158468.
%K cons,nonn
%O 0,1
%A Joseph Biberstine (jrbibers(AT)indiana.edu), Dec 05 2004
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