A270039 a(n) = Smallest m >= 7 containing no threes when represented in any base from 4 through n.

8, 9, 10, 32, 32, 36, 64, 64, 64, 64, 64, 64, 64, 100, 100, 100, 100, 100, 100, 100, 100, 100, 104, 145, 145, 145, 145, 145, 145, 145, 145, 145, 145

Offset: 4

Author

Nathan Fox, Mar 09 2016

Keywords

• nonn
• base
• more

Comments

It remains to be determined if the sequence is finite.

Crossrefs

Cf. A270029, A216192, A270037 - A270045.

Programs

Maple

A270039 := proc(n)
    local m,nothree,b;
    for m from 7 do
        nothree := true;
        for b from 4 to n do
            convert(convert(m,base,b),set) ;
            if 3 in % then
                nothree := false;
                break;
            fi;
        end do:
        if nothree then
            return m;
        end if;
    end do:
end proc: # R. J. Mathar, Mar 11 2016

Mathematica

Table[SelectFirst[Range[7, 10^3], Total@ Map[Function[k, DigitCount[#, k, 3]], Range[4, n]] == 0 &], {n, 7, 60}] /. n_ /; MissingQ@ n -> Nothing (* Michael De Vlieger, Mar 10 2016, Version 10.2 *)