A255805 Numbers with no zeros in base-8 representation.

1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 25, 26, 27, 28, 29, 30, 31, 33, 34, 35, 36, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 49, 50, 51, 52, 53, 54, 55, 57, 58, 59, 60, 61, 62, 63, 73, 74, 75, 76, 77, 78, 79, 81, 82, 83, 84

Offset: 1

Author

Reinhard Zumkeller, Mar 08 2015

Keywords

• nonn
• base
• easy

Comments

Different from A047592, A207481.

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• Wikipedia, Octal
• Index entries for 2-automatic sequences.

Crossrefs

Cf. A007094, A100970 (subsequence).

Zeroless numbers in some other bases <= 10: A000042 (base 2), A032924 (base 3), A023705 (base 4), A248910 (base 6), A255808 (base 9), A052382 (base 10).

Programs

Haskell

a255805 n = a255805_list !! (n-1)
a255805_list = iterate f 1 where
   f x = 1 + if r < 7 then x else 8 * f x'  where (x', r) = divMod x 8

Mathematica

Select[Range[100],DigitCount[#,8,0]==0&] (* Harvey P. Dale, Jun 08 2015 *)

PARI

isok(m) = vecmin(digits(m,8)) > 0; \\ Michel Marcus, Jan 23 2022

Python

def ok(n): return '0' not in oct(n)[2:]
print([k for k in range(85) if ok(k)]) # Michael S. Branicky, Jan 23 2022

Python

from sympy import integer_log
def A255805(n):
    m = integer_log(k:=6*n+1,7)[0]
    return sum(1+(k-7**m)//(6*7**j)%7<<3*j for j in range(m)) # Chai Wah Wu, Jun 28 2025