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

%I #25 Oct 15 2023 05:13:23

%S 45,24885,315,45,340725,196365,15,10965,196365,10465,1652115781968795,

%T 340725,25245,

%U 3976914451825623169001741646052688658398236092769201887156089117865,15345,13695,6232413355673505,79365

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

%C The odd version of A100695.

%H Amiram Eldar, <a href="/A287434/b287434.txt">Table of n, a(n) for n = 1..269</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 = 2, 1-1/(2n+1) = 4/5 = 1/3 + 1/5 + 1/7 + 1/9 + 1/79 + 1/24885, thus a(2) = 24885.

%t 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 Cf. A100695, A286720.

%K nonn

%O 1,1

%A _Amiram Eldar_, May 30 2017