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

1,1

Comments

Complementary sequence to A037465.

Links

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

Example

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.

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)& ]

Prog

(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

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).

Sequence in context: A314242 A107745 A111863 * A043389 A277571 A000966

Adjacent sequences: A333653 A333654 A333655 * A333657 A333658 A333659

Keyword

nonn,base,easy

Author

François Marques, Sep 20 2020

Status

approved