OFFSET
3,1
COMMENTS
See A073101 for more details.
See A257840 for a variant that differs from a(89) on. - M. F. Hasler, Jul 03 2022
LINKS
M. F. Hasler, Table of n, a(n) for n = 3..2000
MAPLE
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
MATHEMATICA
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
PROG
(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
CROSSREFS
KEYWORD
hard,nice,nonn
AUTHOR
T. D. Noe, Sep 10 2002
STATUS
approved