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

Author

Bernard Schott, Feb 18 2023

Keywords

• nonn
• base

Comments

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

Examples

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

Crossrefs

Cf. A000292, A007088, A360573.

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

Programs

Mathematica

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

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

Formula

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