A158469 - OEIS

%I #19 Jul 04 2024 15:14:16

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

%e 1.33274738243289922500860109837389970441674398225984453657972 ...

%p with(numtheory): hz:= limit(1+k -sum(exp(-2^j), j=-k..k), k=infinity): cfrac(evalf(hz, 130), 100, 'quotients')[];

%t 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 Cf. A158468 (decimal expansion), A159835 (Engel expansion).

%K cofr,nonn

%O 0,2

%A _Alois P. Heinz_, Mar 19 2009