A337250 Numbers having at least one 3 in their representation in base 4.

3, 7, 11, 12, 13, 14, 15, 19, 23, 27, 28, 29, 30, 31, 35, 39, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 67, 71, 75, 76, 77, 78, 79, 83, 87, 91, 92, 93, 94, 95, 99, 103, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119

Offset

1,1

Comments

Complementary sequence of A023717.

Links

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

Example

18 is not in the sequence since it is 102_4 in base 4, but 19 is in the sequence since it is 103_4 in base 4.

Maple

seq(`if`(numboccur(3, convert(n, base, 4))>0, n, NULL), n=0..100);

Mathematica

Select[ Range[ 0, 100 ], (Count[ IntegerDigits[ #, 4 ], 3 ]>0)& ]

Prog

(PARI) isok(m) = #select(x->(x==3), digits(m, 4)) >= 1; \\ Michel Marcus, Sep 20 2020
(Python)
from gmpy2 import digits
def A337250(n):
    def f(x):
        l = (s:=digits(x, 4)).find('3')
        if l >= 0: s = s[:l]+'2'*(len(s)-l)
        return n+int(s, 3)
    m, k = n, f(n)
    while m != k: m, k = k, f(k)
    return m # Chai Wah Wu, Dec 04 2024

Crossrefs

Cf. A196032 (at least one 0 in base 4).

Cf. Numbers with at least one digit b-1 in base b : A074940 (b=3), this sequence, A337572 (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: A262505 A083754 A113578 * A043345 A023718 A076184

Adjacent sequences: A337247 A337248 A337249 * A337251 A337252 A337253

Keyword

nonn,base,easy

Author

François Marques, Sep 19 2020

Status

approved