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

1,1

Comments

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

Links

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

Example

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.

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)& ]

Prog

(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

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).

Sequence in context: A290227 A277052 A305496 * A043485 A031495 A224829

Adjacent sequences: A338087 A338088 A338089 * A338091 A338092 A338093

Keyword

nonn,base,easy

Author

François Marques, Oct 09 2020

Status

approved