A338090 Numbers having at least one 8 in their representation in base 9.

8, 17, 26, 35, 44, 53, 62, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 89, 98, 107, 116, 125, 134, 143, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 170, 179, 188, 197, 206, 215, 224, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 251, 260, 269, 278, 287, 296, 305, 314, 315

Offset: 1

Author

François Marques, Oct 09 2020

Keywords

• nonn
• base
• easy

Comments

Blocks of consecutive terms have lengths in A002452. - Devansh Singh, Oct 21 2020

Examples

			70 is not in the sequence since it is 77_9 in base 9, but 76 is in the sequence since it is 84_9 in base 9.
		

Links

• François Marques, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A007095 (base 9).

Complement of A037477.

Cf. A043485 (numbers with exactly one 8 in base 9).

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), this sequence (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), A037477 (b=9), A007095 (b=10), A171397 (b=11).

Programs

Maple

seq(`if`(numboccur(8, convert(n, base, 9))>0, n, NULL), n=0..100);

Mathematica

Select[ Range[ 0, 100 ], (Count[ IntegerDigits[ #, 9 ], 8 ]>0)& ]

PARI

isok(m) = #select(x->(x==8), digits(m, 9)) >= 1;

Python

from gmpy2 import digits
def A338090(n):
    def f(x):
        l = (s:=digits(x,9)).find('8')
        if l >= 0: s = s[:l]+'7'*(len(s)-l)
        return n+int(s,8)
    m, k = n, f(n)
    while m != k: m, k = k, f(k)
    return m # Chai Wah Wu, Dec 04 2024