A255808 Numbers with no zeros in base-9 representation.

1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 16, 17, 19, 20, 21, 22, 23, 24, 25, 26, 28, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 44, 46, 47, 48, 49, 50, 51, 52, 53, 55, 56, 57, 58, 59, 60, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 73, 74, 75

Offset: 1

Author

Reinhard Zumkeller, Mar 08 2015

Keywords

• nonn
• base
• easy

Comments

a(n) = A168183(n) for n <= 72.

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• Index entries for 3-automatic sequences.

Crossrefs

Cf. A007095, A100973 (subsequence).

Zeroless numbers in some other bases <= 10: A000042 (base 2), A032924 (base 3), A023705 (base 4), A248910 (base 6), A255805 (base 8), A052382 (base 10).

Programs

Haskell

a255808 n = a255808_list !! (n-1)
a255808_list = iterate f 1 where
   f x = 1 + if r < 8 then x else 9 * f x'  where (x', r) = divMod x 9

Mathematica

Select[Range[100],DigitCount[#,9,0]==0&] (* or *) With[{upto=100}, Complement[ Range[upto],9*Range[Floor[upto/9]]]] (* Harvey P. Dale, May 29 2019 *)

PARI

isok(n) = vecmin(digits(n, 9)) != 0; \\ Michel Marcus, Jun 29 2019

Python

def A255808(n):
    m = ((k:=7*n+1).bit_length()-1)//3
    return sum((1+((k-(1<<3*m))//(7<<3*j)&7))*9**j for j in range(m)) # Chai Wah Wu, Jun 28 2025