A040870 Continued fraction for sqrt(901).
30, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60
Offset: 0
Examples
30 + 1/(60 + 1/(60 + 1/(60 + 1/(60 + ...)))) = sqrt(901).
Links
Programs
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Maple
with(numtheory): Digits := 300: convert(evalf(sqrt(901)),confrac);
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Mathematica
Block[{$MaxExtraPrecision=1000},ContinuedFraction[Sqrt[901],100]] (* or *) PadRight[{30},100,60] (* Harvey P. Dale, Sep 01 2014 *)
Formula
a(n) = 30*A040000(n). - Stefano Spezia, May 14 2023
From Elmo R. Oliveira, Feb 16 2024: (Start)
a(n) = 60 for n >= 1.
G.f.: 30*(1+x)/(1-x).
E.g.f.: 60*exp(x) - 30. (End)