A040420 Continued fraction for sqrt(442).
21, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42
Offset: 0
Examples
21 + 1/(42 + 1/(42 + 1/(42 + 1/(42 + ...)))) = sqrt(442).
Links
Programs
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Maple
with(numtheory): Digits := 300: convert(evalf(sqrt(442)),confrac);
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Mathematica
Block[{$MaxExtraPrecision=1000}, ContinuedFraction[Sqrt[442],120]] (* or *) PadRight[{21},120,{42}] (* Harvey P. Dale, Nov 28 2024 *)
Formula
From Elmo R. Oliveira, Feb 15 2024: (Start)
a(n) = 42 for n >= 1.
G.f.: 21*(1+x)/(1-x).
E.g.f.: 42*exp(x) - 21.