A040380 Continued fraction for sqrt(401).
20, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40
Offset: 0
Examples
20 + 1/(40 + 1/(40 + 1/(40 + 1/(40 + ...)))) = sqrt(401).
Links
Programs
-
Maple
with(numtheory): Digits := 300: convert(evalf(sqrt(401)),confrac);
Formula
From Elmo R. Oliveira, Feb 15 2024: (Start)
a(n) = 40 for n >= 1.
G.f.: 20*(1+x)/(1-x).
E.g.f.: 40*exp(x) - 20.