A040756 Continued fraction for sqrt(785).
28, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56
Offset: 0
Examples
28 + 1/(56 + 1/(56 + 1/(56 + 1/(56 + ...)))) = sqrt(785).
Links
Programs
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Maple
with(numtheory): Digits := 300: convert(evalf(sqrt(785)),confrac);
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Mathematica
Block[{$MaxExtraPrecision =1000},ContinuedFraction[Sqrt[785],70]] (* or *) PadRight[{28},70,56] (* Harvey P. Dale, May 09 2012 *)
Formula
From Elmo R. Oliveira, Feb 16 2024: (Start)
a(n) = 56 for n >= 1.
G.f.: 28*(1+x)/(1-x).
E.g.f.: 56*exp(x) - 28.