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

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, 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, 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

Offset: 0

Author

Alois P. Heinz, Mar 19 2009

Keywords

• cofr
• nonn

Examples

			1.33274738243289922500860109837389970441674398225984453657972 ...
		

Crossrefs

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

Programs

Maple

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

Mathematica

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 *)