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%I #11 Jan 11 2020 05:35:22
%S 1,2,2,3,4,5,8,11,16,17,77,79,732,733,27538,27539
%N a(2n-1) and a(2n) represent the smallest fraction a(2n-1)/a(2n) needing n unit fractions.
%C Huang Zhibin of China in April 2014 has verified that this fraction (27538/27539) needs 8 unit fractions.
%H Ron Knott, <a href="http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fractions/egyptian.html">Egyptian Fractions</a>
%F a(2n-1) = A097049(n); a(2n) = A097048(n). - _Jon E. Schoenfield_, Jan 11 2020
%e For n=1, 1/2 = 1/2;
%e for n=2, 2/3 = 1/3 + 1/3;
%e for n=3, 4/5 = 1/2 + 1/4 + 1/20 and 4/5 = 1/2 + 1/5 + 1/10;
%e for n=4, 8/11 = 1/2 + 1/6 + 1/22 + 1/66;
%e for n=5, 16/17 = 1/2 + 1/3 + 1/17 + 1/34 + 1/51;
%e for n=6, 77/79 = 1/2 + 1/3 + 1/8 + 1/79 + 1/474 + 1/632;
%e for n=7, 732/733 = 1/2 + 1/3 + 1/7 + 1/45 + 1/7330 + 1/20524 + 1/26388;
%e for n=8, 27538/27539 = 1/2 + 1/3 + 1/7 + 1/43 + 1/1933 + 1/14893663 + 1/1927145066572824 + 1/212829231672162931784; etc.
%Y Cf. A097048, A097049.
%K hard,more,nonn
%O 1,2
%A _Robert G. Wilson v_, Apr 15 2017
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