A360574 Binary expansions of odd numbers with three zeros in their binary expansion.

10001, 100011, 100101, 101001, 110001, 1000111, 1001011, 1001101, 1010011, 1010101, 1011001, 1100011, 1100101, 1101001, 1110001, 10001111, 10010111, 10011011, 10011101, 10100111, 10101011, 10101101, 10110011, 10110101, 10111001, 11000111, 11001011, 11001101, 11010011, 11010101, 11011001, 11100011

Offset

1,1

Comments

For m >= 5, there are A000292(m-4) terms with m digits.

Links

Table of n, a(n) for n=1..32.

Formula

a(n) = A007088(A360573(n)).

Example

1010101 has three digits 0 and is the binary expansion of the odd integer 85, so 1010101 is a term.

Mathematica

FromDigits[IntegerDigits[#, 2]] & /@ Select[Range[1, 250, 2], DigitCount[#, 2, 0] == 3 &] (* Amiram Eldar, Feb 18 2023 *)

Prog

(Python)
from itertools import count, islice
from sympy.utilities.iterables import multiset_permutations
def A360574_gen(): # generator of terms
    yield from (int('1'+''.join(d)+'1') for l in count(0) for d in  multiset_permutations('000'+'1'*l))
A360574_list = list(islice(A360574_gen(), 30)) # Chai Wah Wu, Feb 18 2023

Crossrefs

Cf. A000292, A007088, A360573.

Similar, but with k zeros in their binary expansion: A000042 (k=0), A190619 (k=1), A357774 (k=2).

Sequence in context: A115850 A082567 A364050 * A330135 A031598 A210760

Adjacent sequences: A360571 A360572 A360573 * A360575 A360576 A360577

Keyword

nonn,base

Author

Bernard Schott, Feb 18 2023

Status

approved