A037477 a(n) = Sum{d(i)*9^i: i=0,1,...,m}, where Sum{d(i)*8^i: i=0,1,...,m} is the base 8 representation of n.

0, 1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 16, 18, 19, 20, 21, 22, 23, 24, 25, 27, 28, 29, 30, 31, 32, 33, 34, 36, 37, 38, 39, 40, 41, 42, 43, 45, 46, 47, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 59, 60, 61, 63, 64, 65, 66, 67, 68, 69, 70, 81, 82, 83, 84, 85

Offset: 0

Author

Clark Kimberling

Keywords

• nonn
• base
• easy

Comments

Numbers that do not contain the digit 8 in their base 9 expansion. - M. F. Hasler, Oct 05 2014

Examples

			a(63) = 7*9+7 = 70 since 63 = 77[8], i.e., "77" when written in base 8;
a(64) = 1*9^2 = 81 since 64 = 100[8]. - _M. F. Hasler_, Oct 05 2014
		

Links

• François Marques, Table of n, a(n) for n = 0..10000 (first 1000 terms from Clark Kimberling)

Crossrefs

Cf. A248375.

Cf. Numbers with at least one digit b-1 in base b : A074940 (b=3), A337250 (b=4), A337572 (b=5), A333656 (b=6), A337141 (b=7), A337239 (b=8), A338090 (b=9), A011539 (b=10), A095778 (b=11).

Cf. Numbers with no digit b-1 in base b: A005836 (b=3), A023717 (b=4), A020654 (b=5), A037465 (b=6), A020657 (b=7), A037474 (b=8), this sequence (b=9), A007095 (b=10), A171397 (b=11).

Programs

Mathematica

Table[FromDigits[RealDigits[n, 8], 9], {n, 0, 100}]
Select[Range[0,100],DigitCount[#,9,8]==0&] (* Harvey P. Dale, Aug 06 2024 *)

PARI

a(n) = vector(#n=digits(n,8),i,9^(#n-i))*n~ \\ M. F. Hasler, Oct 05 2014

PARI

a(n) = fromdigits(digits(n, 8), 9); \\ François Marques, Oct 15 2020

Python

def A037477(n): return int(oct(n)[2:],9) # Chai Wah Wu, Jan 27 2025

Formula

For n<64, a(n) = floor(9n/8) = A248375(n). - M. F. Hasler, Oct 05 2014

Extensions

Offset changed to 0 by Clark Kimberling, Aug 14 2012