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A158469 Continued fraction for hz = limit_{k -> infinity} 1 + k - Sum_{j = -k..k} exp(-2^j).

%I A158469 #19 Jul 04 2024 15:14:16
%S A158469 1,3,189,3,2,2,1,5,4,1,1,3,1,1,1,5,8,12,1,22,7,14,1,2,1,5,1,4,222,1,1,
%T A158469 2,3,24,6,27,1,15,1,9,1,1,18,6,24,2,1,7,1,4,2,2,1,1,84,1,1,1,3,1,1,1,
%U A158469 1,1,5,15,3,13,3,2,14,1,1,1,10,15,10,1,6,120,1,31,2,4,2,7,2,2,1,1,1,1,1,3,7
%N A158469 Continued fraction for hz = limit_{k -> infinity} 1 + k - Sum_{j = -k..k} exp(-2^j).
%e A158469 1.33274738243289922500860109837389970441674398225984453657972 ...
%p A158469 with(numtheory): hz:= limit(1+k -sum(exp(-2^j), j=-k..k), k=infinity): cfrac(evalf(hz, 130), 100, 'quotients')[];
%t A158469 terms = 95; digits = terms+15; 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++]; hz = FromDigits[f[n]]*10^-digits; ContinuedFraction[hz, terms] (* _Jean-François Alcover_, Mar 23 2017 *)
%Y A158469 Cf. A158468 (decimal expansion), A159835 (Engel expansion).
%K A158469 cofr,nonn
%O A158469 0,2
%A A158469 _Alois P. Heinz_, Mar 19 2009