A040506 Continued fraction for sqrt(530).
23, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46
Offset: 0
Examples
23 + 1/(46 + 1/(46 + 1/(46 + 1/(46 + ...)))) = sqrt(530).
Links
Programs
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Maple
with(numtheory): Digits := 300: convert(evalf(sqrt(530)),confrac);
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Mathematica
Block[{$MaxExtraPrecision=1000}, ContinuedFraction[Sqrt[530],100]] (* or *) PadRight[{23},100,{46}] (* Harvey P. Dale, Jul 14 2024 *)
Formula
From Elmo R. Oliveira, Feb 15 2024: (Start)
a(n) = 46 for n >= 1.
G.f.: 23*(1+x)/(1-x).
E.g.f.: 46*exp(x) - 23.
a(n) = 23*A040000(n). (End)