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A360574 Binary expansions of odd numbers with three zeros in their binary expansion. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
For m >= 5, there are A000292(m-4) terms with m digits.
LINKS
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
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
KEYWORD
nonn,base
AUTHOR
Bernard Schott, Feb 18 2023
STATUS
approved

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)