A043698 Numbers whose base-9 representation has an even number of runs.

9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 22, 23, 24, 25, 26, 27, 28, 29, 31, 32, 33, 34, 35, 36, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 48, 49, 51, 52, 53, 54, 55, 56, 57, 58, 59, 61, 62, 63, 64, 65, 66, 67, 68, 69, 71, 72, 73, 74, 75, 76, 77, 78, 79, 81, 90, 92, 93, 94, 95, 96, 97, 98, 101, 111, 121, 131, 141

Offset: 1

Author

Clark Kimberling

Keywords

• nonn
• base

Programs

Maple

isA043698 := proc(n)
    local dgs,runs,i ;
    dgs := convert(n,base,9) ;
    runs :=1 ;
    for i from 2 to nops(dgs) do
        if op(i,dgs) <> op(i-1,dgs) then
            runs := runs+1 ;
        end if;
    end do:
    if type(runs,'even') then
        true;
    else
        false;
    end if;
end proc:
A043698 := proc(n)
    option remember;
    local a;
    if n = 1 then
        9;
    else
        for a from procname(n-1)+1 do
            if isA043698(a) then
                return a ;
            end if;
        end do:
    end if
end proc:
seq(A043698(n),n=1..120) ; # R. J. Mathar, Feb 20 2023