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.

89, 113, 161, 233, 281, 329, 353, 401, 409, 449, 473, 521, 593, 641, 689, 713, 761, 769, 809, 929, 953, 1049, 1073, 1121, 1129, 1169, 1193, 1241, 1249, 1313, 1321, 1361, 1369, 1409, 1433, 1481, 1513, 1529, 1553, 1561, 1601, 1609, 1649, 1673, 1721, 1769

Offset: 1

Author

M. F. Hasler, May 16 2015

Keywords

• nonn
• hard

Comments

Related to the Erdős-Straus conjecture, see A073101 for more details.

This lists indices for which (A075245, A075246, A075247) differ from (A257839, A257840, A257841).

Examples

			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.
		

Links

• Manfred Scheucher, Table of n, a(n) for n = 1..62

Crossrefs

Cf. A073101, A075245, A075246, A075247, A257839, A257840, A257841.

Programs

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
				

Extensions

More terms from Manfred Scheucher, May 24 2015