A257840 y-value of the lexicographically first integer solution (x,y,z) of 4/n = 1/x + 1/y + 1/z with 0 < x < y < z, or 0 if there is no such solution. Corresponding x and z values are in A257839 and A257841.

0, 0, 4, 3, 4, 7, 15, 7, 10, 16, 34, 13, 18, 29, 61, 21, 30, 46, 96, 31, 43, 67, 139, 43, 60, 92, 190, 57, 78, 121, 249, 73, 100, 154, 316, 91, 124, 191, 391, 111, 154, 232, 474, 133, 181, 277, 565, 157, 99, 326, 664, 183, 248, 379, 771, 211, 286, 436, 886, 241, 326, 497, 1009, 273, 370, 562, 1140, 307, 415, 631, 1279, 343, 210, 704, 1426, 381, 514, 781, 1581, 421

Offset: 1

Author

M. F. Hasler, May 16 2015

Keywords

• nonn

Comments

See A073101 for more details.

This differs from A075246 starting with a(89)=690 vs A075246(89)=306, corresponding to the representations 4/89 = 1/23 + 1/690 + 1/61410 = 1/24 + 1/306 + 1/108936.

Links

• M. F. Hasler, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A073101, A075245, A075246, A075247.

Programs

PARI

apply( {A257840(n, t)=for(x=n\4+1, 3*n\4, for(y=max(1\t=4/n-1/x, x)+1, ceil(2/t)-1, numerator(t-1/y)==1 && return(y)))}, [1..99]) \\ improved by M. F. Hasler, Jul 03 2022