A337572 Numbers having at least one 4 in their representation in base 5.

4, 9, 14, 19, 20, 21, 22, 23, 24, 29, 34, 39, 44, 45, 46, 47, 48, 49, 54, 59, 64, 69, 70, 71, 72, 73, 74, 79, 84, 89, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 129, 134

Offset

1,1

Comments

Complementary sequence to A020654.

Links

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

Example

75 is not in the sequence since it is 300_5 in base 5, but 74 is in the sequence since it is 244_5 in base 5.

Maple

seq(`if`(numboccur(4, convert(n, base, 5))>0, n, NULL), n=0..100);

Mathematica

Select[ Range[ 0, 100 ], (Count[ IntegerDigits[ #, 5 ], 4 ]>0)& ]

Prog

(PARI) isok(m) = #select(x->(x==4), digits(m, 5)) >= 1; \\ Michel Marcus, Sep 20 2020
(Python)
from gmpy2 import digits
def A337572(n):
    def f(x):
        l = (s:=digits(x, 5)).find('4')
        if l >= 0: s = s[:l]+'3'*(len(s)-l)
        return n+int(s, 4)
    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), this sequence (b=5), A333656 (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: A313080 A313081 A100213 * A043365 A023738 A070799

Adjacent sequences: A337569 A337570 A337571 * A337573 A337574 A337575

Keyword

nonn,base,easy

Author

François Marques, Sep 19 2020

Status

approved