OFFSET
1,2
COMMENTS
Curiously, this constant is close to gamma/log(2)+1/2 = 1.332746177... - Jean-François Alcover, Mar 24 2014
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..1000
FORMULA
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
Also equals limit_{k->oo} 1 + Sum_{j>=1} 1-(1-1/2^j)^(2^k). - Toshitaka Suzuki, Feb 12 2017
EXAMPLE
1.3327473824328992250086010983738997044167439822598445365797...
MAPLE
hz:= limit(1+k -sum(exp(-2^j), j=-k..k), k=infinity):
hzs:= convert(evalf(hz/10, 130), string):
seq(parse(hzs[n+1]), n=1..120);
MATHEMATICA
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 *)
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Alois P. Heinz, Mar 19 2009
STATUS
approved