A248910 Numbers with no zeros in base-6 representation.

1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 19, 20, 21, 22, 23, 25, 26, 27, 28, 29, 31, 32, 33, 34, 35, 43, 44, 45, 46, 47, 49, 50, 51, 52, 53, 55, 56, 57, 58, 59, 61, 62, 63, 64, 65, 67, 68, 69, 70, 71, 79, 80, 81, 82, 83, 85, 86, 87, 88, 89, 91, 92

Offset: 1

Author

Reinhard Zumkeller, Mar 08 2015

Keywords

• nonn
• base
• easy

Comments

Different from A039215, A047253, A184522, A187390, A194386.

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• Wikipedia, Senary
• Index entries for 6-automatic sequences.

Crossrefs

Cf. A007092, A100969 (subsequence).

Zeroless numbers in some other bases <= 10: A000042 (base 2), A032924 (base 3), A023705 (base 4), A255805 (base 8), A255808 (base 9), A052382 (base 10).

Programs

Haskell

a248910 n = a248910_list !! (n-1)
a248910_list = iterate f 1 where
   f x = 1 + if r < 5 then x else 6 * f x'  where (x', r) = divMod x 6

Mathematica

Select[Range[100], DigitCount[#,6, 0] == 0 &] (* Paolo Xausa, Jun 29 2025 *)

PARI

isok(m) = vecmin(digits(m, 6)) > 0; \\ Michel Marcus, Jan 23 2022

Python

from sympy import integer_log
def A248910(n):
    m = integer_log(k:=(n<<2)+1,5)[0]
    return sum((1+(k-5**m)//(5**j<<2)%5)*6**j for j in range(m)) # Chai Wah Wu, Jun 28 2025