A040342 Continued fraction for sqrt(362).
19, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38
Offset: 0
Examples
19 + 1/(38 + 1/(38 + 1/(38 + 1/(38 + ...)))) = sqrt(362).
Links
Programs
-
Maple
with(numtheory): Digits := 300: convert(evalf(sqrt(362)),confrac);
Formula
From Elmo R. Oliveira, Feb 14 2024: (Start)
a(n) = 38 for n >= 1.
G.f.: 19*(1+x)/(1-x).
E.g.f.: 38*exp(x) - 19.
a(n) = 19*A040000(n). (End)