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A075246 y-value of the solution (x,y,z) to 4/n = 1/x + 1/y + 1/z satisfying 0 < x < y < z and having the largest z-value. The x and z components are in A075245 and A075247.

%I A075246 #19 Jul 04 2022 04:45:10
%S A075246 4,3,4,7,15,7,10,16,34,13,18,29,61,21,30,46,96,31,43,67,139,43,60,92,
%T A075246 190,57,78,121,249,73,100,154,316,91,124,191,391,111,154,232,474,133,
%U A075246 181,277,565,157,99,326,664,183,248,379,771,211,286,436,886,241,326
%N A075246 y-value of the solution (x,y,z) to 4/n = 1/x + 1/y + 1/z satisfying 0 < x < y < z and having the largest z-value. The x and z components are in A075245 and A075247.
%C A075246 See A073101 for more details.
%C A075246 See A257840 for a variant that differs from a(89) on. - _M. F. Hasler_, Jul 03 2022
%H A075246 M. F. Hasler, <a href="/A075246/b075246.txt">Table of n, a(n) for n = 3..2000</a>
%p A075246 A075246:=proc() local t, n,a,b,t1,largey,largez; for n from 3 to 100 do t:=4/n; largez:=0; largey:=0; for a from floor(1/t)+1 to floor(3/t) do t1:=t - 1/a; for b from max(a,floor(1/t1)+1) to floor(2/(t1)) do if and(type(1/(t1 - 1/b),integer),a<b,b<(1/(t1 - 1/b))) then if (1/(t1 - 1/b))>largez then largez:=(1/(t1 - 1/b)); largey:=b; end if end if end do; end do; lprint(n, largey) end do; end proc; # [program derived from A192787] _Patrick J. McNab_, Aug 20 2014
%t A075246 For[xLst={}; yLst={}; zLst={}; n=3, n<=100, n++, cnt=0; xr=n/4; If[IntegerQ[xr], x=xr+1, x=Ceiling[xr]]; While[yr=1/(4/n-1/x); If[IntegerQ[yr], y=yr+1, y=Ceiling[yr]]; cnt==0&&y>x, While[zr=1/(4/n-1/x-1/y); cnt==0&&zr>y, If[IntegerQ[zr], z=zr; cnt++; AppendTo[xLst, x]; AppendTo[yLst, y]; AppendTo[zLst, z]]; y++ ]; x++ ]]; yLst
%o A075246 (PARI) apply( {A075246(n, c=1, a, t)=for(x=n\4+1, 3*n\4, for(y=max(1\t=4/n-1/x, x)+1, ceil(2/t)-1, t-1/y >= c && break; numerator(t-1/y)==1 && [c, a]=[t-1/y, y])); a}, [3..99]) \\ _M. F. Hasler_, Jul 03 2022
%Y A075246 Cf. A073101 (number of solutions), A075245 (x values), A075247 (z values), A192787 (number of solutions with x <= y <= z), A257840 (variant: lex earliest solution, not largest z).
%K A075246 hard,nice,nonn
%O A075246 3,1
%A A075246 _T. D. Noe_, Sep 10 2002