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%I #32 Oct 15 2023 05:13:42
%S 4,6,6,4,6,6,4,6,6,6,8,6,6,10,6,6,8,6,12,10,10,4,6,6,6,8,6,6,8,10,6,6,
%T 8,8,6,10,6,8,6,8,6,10,6,10,6,10,6,10,6,8,8,6,8,8,8,6,6,6,10,8,6,8,10,
%U 12,8,10,6,8,8,8,10,8,6,8,10,6,8,8,6,6,8
%N Number of Egyptian fractions in the representation of 1-1/(2n+1) by the odd greedy expansion algorithm, without repeats.
%C The odd version of A100678.
%H Amiram Eldar, <a href="/A286720/b286720.txt">Table of n, a(n) for n = 1..10000</a>
%H Kevin Brown, <a href="http://www.mathpages.com/home/kmath478.htm">Odd-Greedy Unit Fraction Expansions</a>.
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Odd_greedy_expansion">Odd greedy expansion</a>.
%e For n = 1, 1-1/(2n+1) = 2/3 = 1/3 + 1/5 + 1/9 + 1/45 has 4 fractions in the representation, thus a(1) = 4.
%t odd[n_]:=If[OddQ[n],n,n+1];a={};For[n=0,n<100,n++;lst={};k=2n/(2n+1);s1=0; While[k>0,s2=odd[Ceiling[1/k]]; If[s2==s1,s2+=2]; AppendTo[lst, s2]; k=k-1/s2; s1=s2];a=AppendTo[a,Length[lst]]];a
%Y Cf. A100678.
%K nonn
%O 1,1
%A _Amiram Eldar_, May 30 2017
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