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A287434 Largest denominator used in the Egyptian fraction representation of 1-1/(2n+1) by the odd greedy expansion algorithm, without repeats.

%I A287434 #25 Oct 15 2023 05:13:23
%S A287434 45,24885,315,45,340725,196365,15,10965,196365,10465,1652115781968795,
%T A287434 340725,25245,
%U A287434 3976914451825623169001741646052688658398236092769201887156089117865,15345,13695,6232413355673505,79365
%N A287434 Largest denominator used in the Egyptian fraction representation of 1-1/(2n+1) by the odd greedy expansion algorithm, without repeats.
%C A287434 The odd version of A100695.
%H A287434 Amiram Eldar, <a href="/A287434/b287434.txt">Table of n, a(n) for n = 1..269</a>
%H A287434 Kevin Brown, <a href="http://www.mathpages.com/home/kmath478.htm">Odd-Greedy Unit Fraction Expansions</a>.
%H A287434 Wikipedia, <a href="http://en.wikipedia.org/wiki/Odd_greedy_expansion">Odd greedy expansion</a>.
%e A287434 For n = 2, 1-1/(2n+1) = 4/5 = 1/3 + 1/5 + 1/7 + 1/9 + 1/79 + 1/24885, thus a(2) = 24885.
%t A287434 odd[n_]:=If[OddQ[n],n,n+1];a={};For[n=0,n<100,n++;dlast=0;k=2n/(2n+1);s1=0; While[k>0,s2=odd[Ceiling[1/k]]; If[s2==s1,s2+=2]; dlast=s2; k=k-1/s2; s1=s2];a=AppendTo[a,dlast]];a
%Y A287434 Cf. A100695, A286720.
%K A287434 nonn
%O A287434 1,1
%A A287434 _Amiram Eldar_, May 30 2017