A033032 Numbers all of whose base 6 digits are odd.

1, 3, 5, 7, 9, 11, 19, 21, 23, 31, 33, 35, 43, 45, 47, 55, 57, 59, 67, 69, 71, 115, 117, 119, 127, 129, 131, 139, 141, 143, 187, 189, 191, 199, 201, 203, 211, 213, 215, 259, 261, 263, 271, 273, 275, 283, 285, 287, 331, 333, 335, 343

Offset: 1

Author

Clark Kimberling

Keywords

• nonn
• base

Links

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

Programs

Maple

g:= proc(t,d) local L;
    L:= convert(3^d+t,base,3);
    add((2*L[i]+1)*6^(i-1),i=1..d);
end proc:
seq(seq(g(t,d),t=0..3^d-1),d=1..4); # Robert Israel, Aug 16 2018

Mathematica

Table[FromDigits[#,6]&/@Tuples[{1,3,5},n],{n,4}]//Flatten (* Harvey P. Dale, Dec 24 2022 *)

PARI

isok(n) = (n) && (#select(x->((x%2)==0), digits(n, 6)) == 0); \\ Michel Marcus, Aug 17 2018

Formula

If (3^d-1)/2 <= n < (3^(d+1)-1)/2, then a(n+3^d) = a(n) + 6^n, a(n+2*3^d) = a(n) + 2*6^n, and a(n+3^(d+1)) = a(n) + 5*6^n. - Robert Israel, Aug 16 2018