cp's OEIS Frontend

A257843 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.

%I A257843 #28 May 08 2020 03:39:00
%S A257843 89,113,161,233,281,329,353,401,409,449,473,521,593,641,689,713,761,
%T A257843 769,809,929,953,1049,1073,1121,1129,1169,1193,1241,1249,1313,1321,
%U A257843 1361,1369,1409,1433,1481,1513,1529,1553,1561,1601,1609,1649,1673,1721,1769
%N A257843 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 A257843 Related to the Erdős-Straus conjecture, see A073101 for more details.
%C A257843 This lists indices for which (A075245, A075246, A075247) differ from (A257839, A257840, A257841).
%H A257843 Manfred Scheucher, <a href="/A257843/b257843.txt">Table of n, a(n) for n = 1..62</a>
%e A257843 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 A257843 (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 A257843 Cf. A073101, A075245, A075246, A075247, A257839, A257840, A257841.
%K A257843 nonn,hard
%O A257843 1,1
%A A257843 _M. F. Hasler_, May 16 2015
%E A257843 More terms from _Manfred Scheucher_, May 24 2015