A031959 Numbers with exactly three distinct base-7 digits.

51, 52, 53, 54, 55, 63, 66, 67, 68, 69, 70, 72, 74, 75, 76, 77, 79, 80, 82, 83, 84, 86, 87, 88, 90, 91, 93, 94, 95, 96, 99, 101, 102, 103, 104, 105, 108, 109, 110, 111, 119, 120, 123, 124, 125, 126, 127, 129, 131, 132, 133, 134, 136

Offset: 1

Author

Clark Kimberling

Keywords

• nonn
• base

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A007093.

Programs

Maple

f:= proc(d)  uses combinat; local S,Res,A1,A1p,A2,x1,x2;
     Res:= NULL:
     for S in choose({$0..6},3) do
       x1:= S[3]*(7^d-1)/6;
       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(7^(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(7^(j-1),j=A2);
         od
       od
     od;
     sort([Res]);
end proc:
op(f(3)),op(f(4)); # Robert Israel, Oct 29 2018

Mathematica

Select[Range[150],Length[Union[IntegerDigits[#,7]]]==3&] (* Harvey P. Dale, Mar 29 2019 *)