|
%I #40 Nov 30 2020 18:46:19
%S 1,3,3,2,7,4,7,3,8,2,4,3,2,8,9,9,2,2,5,0,0,8,6,0,1,0,9,8,3,7,3,8,9,9,
%T 7,0,4,4,1,6,7,4,3,9,8,2,2,5,9,8,4,4,5,3,6,5,7,9,7,1,8,4,9,3,9,9,3,3,
%U 4,1,6,8,8,2,7,3,5,4,7,4,5,4,0,7,0,2,8,0,6,5,1,7,1,6,6,6,0,4,7,8,7,0,4,0,6,6,8,5
%N Decimal expansion of hz = limit_{k -> infinity} 1 + k - Sum_{j = -k..k} exp(-2^j).
%C Curiously, this constant is close to gamma/log(2)+1/2 = 1.332746177... - _Jean-François Alcover_, Mar 24 2014
%H Alois P. Heinz, <a href="/A158468/b158468.txt">Table of n, a(n) for n = 1..1000</a>
%F Equals gamma/log(2)+1/2 + Sum_{k>=1} Im(Gamma(1-2*k*Pi*i/log(2)))/(k*Pi). - _Toshitaka Suzuki_, Feb 10 2017
%F Also equals limit_{k->oo} 1 + Sum_{j>=1} 1-(1-1/2^j)^(2^k). - _Toshitaka Suzuki_, Feb 12 2017
%e 1.3327473824328992250086010983738997044167439822598445365797...
%p hz:= limit(1+k -sum(exp(-2^j), j=-k..k), k=infinity):
%p hzs:= convert(evalf(hz/10, 130), string):
%p seq(parse(hzs[n+1]), n=1..120);
%t digits = 105; Clear[f]; f[k_] := f[k] = 1 + k - Sum[Exp[-2^j], {j, -k, k}] // RealDigits[#, 10, digits+1]& // First // Quiet; f[1]; f[n=2]; While[f[n] != f[n-1], n++] ; f[n] // Most (* _Jean-François Alcover_, Feb 19 2013 *)
%Y Cf. A100668 (gamma/log(2)), A158469 (continued fraction), A159835 (Engel expansion), A339168.
%K nonn,cons
%O 1,2
%A _Alois P. Heinz_, Mar 19 2009
|
