A257841 - OEIS

%I #14 Jul 03 2022 22:14:40

%S 0,0,12,6,20,42,210,42,90,240,1122,156,468,812,3660,420,510,2070,9120,

%T 930,1806,4422,19182,1806,2100,8372,35910,3192,9048,14520,61752,5256,

%U 9900,23562,99540,8190,22940,36290,152490,12210,6314,53592,224202,17556,32580,76452,318660,24492,9702,105950,440232,33306,92008,143262,593670,44310,81510,189660,784110,57840

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

%C See A073101 for more details.

%C This differs from A075247 starting with a(89) = 61410 vs. A075247(89) = 108936, corresponding to the representations 4/89 = 1/23 + 1/690 + 1/61410 = 1/24 + 1/306 + 1/108936.

%H M. F. Hasler, <a href="/A257841/b257841.txt">Table of n, a(n) for n = 1..1000</a>

%o (PARI) apply( {A257841(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/(t*y-1))))}, [1..99]) \\ improved by _M. F. Hasler_, Jul 03 2022

%Y Cf. A073101, A075245, A075246, A075247.

%K nonn

%O 1,3

%A _M. F. Hasler_, May 16 2015