A333656 Numbers having at least one 5 in their representation in base 6.

5, 11, 17, 23, 29, 30, 31, 32, 33, 34, 35, 41, 47, 53, 59, 65, 66, 67, 68, 69, 70, 71, 77, 83, 89, 95, 101, 102, 103, 104, 105, 106, 107, 113, 119, 125, 131, 137, 138, 139, 140, 141, 142, 143, 149, 155, 161, 167, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184

Offset: 1

Author

François Marques, Sep 20 2020

Keywords

• nonn
• base
• easy

Comments

Complementary sequence to A037465.

Examples

			22 is not in the sequence since it is 34_6 in base 6, but 23 is in the sequence since it is 35_6 in base 6.
		

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

Programs

Maple

seq(`if`(numboccur(5, convert(n, base, 6))>0, n, NULL), n=0..100);

Mathematica

Select[ Range[ 0, 100 ], (Count[ IntegerDigits[ #, 6 ], 5 ]>0)& ]

PARI

isok(m) = #select(x->(x==5), digits(m, 6)) >= 1;

Python

from gmpy2 import digits
def A333656(n):
    def f(x):
        l = (s:=digits(x,6)).find('5')
        if l >= 0: s = s[:l]+'4'*(len(s)-l)
        return n+int(s,5)
    m, k = n, f(n)
    while m != k: m, k = k, f(k)
    return m # Chai Wah Wu, Dec 04 2024