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

Author

François Marques, Sep 20 2020

Keywords

• nonn
• base
• easy

Comments

Complementary sequence to A020657.

Examples

			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.
		

Links

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

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).

Programs

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 *)

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