@Mathematica
romanNumeralMax[n_]:=Module[{romanNumeral,lst,maxlength},
(* Function *)
romanNumeral[nx_]:=Module[{nToRoman,nnToRoman,nnnToRoman,nnnnToRoman},
nToRoman[mx_]:=mx//
Which[
#==0,"",
#==1,"I",
#==2,"II",
#==3,"III",
#==4,"IV",
#==5,"V",
#==6,"VI",
#==7,"VII",
#==8,"VIII",
#==9,"IX",
True,""]&;
nnToRoman[mx_]:=mx//
nToRoman//
StringReplace[#,{"I"->"X","V"->"L","X"->"C"}]&;
nnnToRoman[mx_]:=mx//
nToRoman//
StringReplace[#,{"I"->"C","V"->"D","X"->"M"}]&;
nnnnToRoman[mx_]:=mx//
nToRoman//
StringReplace[#,{"I"->"M","V"->"*","X"->"*"}]&;
nx//
IntegerDigits//
PadLeft[#,4]&//
{nnnnToRoman[#[[1]]],nnnToRoman[#[[2]]],nnToRoman[#[[3]]],nToRoman[#[[4]]]}&//
StringJoin
];
(* Data & Parameter *)
lst=n//
Range//
Map[{#,romanNumeral[#]}&,#]&//
Map[{#[[1]],StringLength[#[[2]]]}&,#]&;
maxlength=lst//
Map[#[[2]]&,#]&//
Max;
(* Results *)
lst//
Select[#,#[[2]]==maxlength&]&//
Map[#[[1]]&,#]&
];
In[1] := romanNumeralMax[1887]
Out[1] = {888, 1388, 1788, 1838, 1878, 1883, 1887}
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