A031962 Numbers with exactly three distinct base-10 digits.

102, 103, 104, 105, 106, 107, 108, 109, 120, 123, 124, 125, 126, 127, 128, 129, 130, 132, 134, 135, 136, 137, 138, 139, 140, 142, 143, 145, 146, 147, 148, 149, 150, 152, 153, 154, 156, 157, 158, 159, 160, 162, 163, 164, 165, 167, 168, 169, 170, 172, 173, 174

Offset: 1

Author

Clark Kimberling

Keywords

• nonn
• base

Links

• Robert Israel, Table of n, a(n) for n = 1..10000 (first 648 terms from T. D. Noe)

Crossrefs

Cf. A031956, A031957, A031958, A031959, A031960, A031961.

Programs

Maple

f:= proc(d,b)  uses combinat; local S,Res,A1,A1p,A2,x1,x2;
     Res:= NULL:
     for S in choose({$0..b-1},3) do
       x1:= S[3]*(b^d-1)/(b-1);
       for A1 in powerset(d) minus {{}} do
         if S[1]=0 and member(d,A1) then next fi;
         x2:= x1 + (S[1]-S[3])*add(b^(j-1),j=A1);
         A1p:= {$1..d} minus A1;
         for A2 in powerset(A1p) minus {{},A1p} do
           Res:= Res, x2 + (S[2]-S[3])*add(b^(j-1),j=A2);
         od
       od
     od;
     op(sort([Res]));
end proc:
f(3,10),f(4,10); # Robert Israel, Oct 29 2018

Mathematica

Select[Range[100, 200], Length[Union[IntegerDigits[#]]] == 3 &] (* T. D. Noe, Dec 04 2012 *)
Select[Range[100,200],Count[DigitCount[#],0]==7&] (* Harvey P. Dale, May 22 2020 *)

PARI

isok(n) = #Set(digits(n)) == 3; \\ Michel Marcus, Oct 29 2018

Extensions

Edited by Robert Israel, Oct 29 2018