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%I #28 May 08 2020 03:39:00
%S 89,113,161,233,281,329,353,401,409,449,473,521,593,641,689,713,761,
%T 769,809,929,953,1049,1073,1121,1129,1169,1193,1241,1249,1313,1321,
%U 1361,1369,1409,1433,1481,1513,1529,1553,1561,1601,1609,1649,1673,1721,1769
%N Numbers n for which the lexicographically first integer solution (x,y,z) of 4/n = 1/x + 1/y + 1/z with 0 < x < y < z, is different from the solution having the largest z-value.
%C Related to the Erdős-Straus conjecture, see A073101 for more details.
%C This lists indices for which (A075245, A075246, A075247) differ from (A257839, A257840, A257841).
%H Manfred Scheucher, <a href="/A257843/b257843.txt">Table of n, a(n) for n = 1..62</a>
%e For n=89, 4/89 = 1/23 + 1/690 + 1/61410 = 1/24 + 1/306 + 1/108936 are the representations with the largest resp. smallest unit fraction.
%o (PARI) is(n,s=0)=for(c=n\4+1,n*3\4,for(b=c+1,ceil(2/(t=4/n-1/c))-1,numerator(t-1/b)==1||next;!s&&(s=t-1/b)&&next(2);t-1/b<s&&return(1)))
%Y Cf. A073101, A075245, A075246, A075247, A257839, A257840, A257841.
%K nonn,hard
%O 1,1
%A _M. F. Hasler_, May 16 2015
%E More terms from _Manfred Scheucher_, May 24 2015