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Egyptian fraction representation of sqrt(20) (A010476) using a greedy function.
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%I #6 Oct 20 2019 12:35:35

%S 4,3,8,73,9617,111131795,26084503201670555,

%T 4157115685705509978962832510685264,

%U 147322611763368949503218439363472434087529649552239912252006589221170,71615688159358613181735412731094718668653530665367791449989367208307390123881747858538896669229709245658779872053034609094278277577821587

%N Egyptian fraction representation of sqrt(20) (A010476) using a greedy function.

%t Egyptian[nbr_] := Block[{lst = {IntegerPart[nbr]}, cons = N[ FractionalPart[ nbr], 2^20], denom, iter = 8}, While[ iter > 0, denom = Ceiling[ 1/cons]; AppendTo[ lst, denom]; cons -= 1/denom; iter--]; lst]; Egyptian[ Sqrt[ 20]]

%Y Egyptian fraction representations of the square roots: A006487, A224231, A248235-A248322.

%Y Egyptian fraction representations of the cube roots: A129702, A132480-A132574.

%K nonn

%O 0,1

%A _Robert G. Wilson v_, Oct 04 2014