A337141 Numbers having at least one 6 in their representation in base 7.

6, 13, 20, 27, 34, 41, 42, 43, 44, 45, 46, 47, 48, 55, 62, 69, 76, 83, 90, 91, 92, 93, 94, 95, 96, 97, 104, 111, 118, 125, 132, 139, 140, 141, 142, 143, 144, 145, 146, 153, 160, 167, 174, 181, 188, 189, 190, 191, 192, 193, 194, 195, 202, 209, 216, 223, 230, 237, 238, 239, 240

Offset

1,1

Comments

Complementary sequence to A020657.

Links

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

Example

33 is not in the sequence since it is 45_7 in base 7, but 34 is in the sequence since it is 46_7 in base 7.

Maple

seq(`if`(numboccur(6, convert(n, base, 7))>0, n, NULL), n=0..100);

Mathematica

Select[ Range[ 0, 100 ], (Count[ IntegerDigits[ #, 7 ], 6 ]>0)& ]
Select[Range[300], DigitCount[#, 7, 6]>0&] (* Harvey P. Dale, Dec 23 2020 *)

Prog

(PARI) isok(m) = #select(x->(x==6), digits(m, 7)) >= 1;
(Python)
from gmpy2 import digits
def A337141(n):
    def f(x):
        l = (s:=digits(x, 7)).find('6')
        if l >= 0: s = s[:l]+'5'*(len(s)-l)
        return n+int(s, 6)
    m, k = n, f(n)
    while m != k: m, k = k, f(k)
    return m # Chai Wah Wu, Dec 04 2024

Crossrefs

Cf. Numbers with at least one digit b-1 in base b: A074940 (b=3), A337250 (b=4), A337572 (b=5), A333656 (b=6), this sequence (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), A037477 (b=9), A007095 (b=10), A171397 (b=11).

Sequence in context: A048929 A187393 A356059 * A043417 A031485 A004919

Adjacent sequences: A337138 A337139 A337140 * A337142 A337143 A337144

Keyword

nonn,base,easy

Author

François Marques, Sep 20 2020

Status

approved