A037477 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

COMMENTS

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

LINKS

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

FORMULA

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

EXAMPLE

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

MATHEMATICA

Table[FromDigits[RealDigits[n, 8], 9], {n, 0, 100}]

Select[Range[0, 100], DigitCount[#, 9, 8]==0&] (* Harvey P. Dale, Aug 06 2024 *)

PROG

(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

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).

Sequence in context: A171524 A052421 A248375 * A277050 A013937 A118065

Adjacent sequences: A037474 A037475 A037476 * A037478 A037479 A037480

KEYWORD

nonn,base,easy

AUTHOR

Clark Kimberling

EXTENSIONS

Offset changed to 0 by Clark Kimberling, Aug 14 2012

STATUS

approved