A357774 Binary expansions of odd numbers with two zeros in their binary expansion.

1001, 10011, 10101, 11001, 100111, 101011, 101101, 110011, 110101, 111001, 1001111, 1010111, 1011011, 1011101, 1100111, 1101011, 1101101, 1110011, 1110101, 1111001, 10011111, 10101111, 10110111, 10111011, 10111101, 11001111, 11010111, 11011011, 11011101, 11100111, 11101011

Offset

1,1

Comments

For m >= 4, there are A000217(m-3) terms with m digits.

Links

Table of n, a(n) for n=1..31.

Formula

a(n) = A007088(A357773(n)).

Mathematica

FromDigits[IntegerDigits[#, 2]] & /@ Select[Range[1, 250, 2], DigitCount[#, 2, 0] == 2 &] (* Amiram Eldar, Oct 19 2022 *)

Prog

(Python)
from itertools import combinations, count, islice
def agen(): # generator of terms
    for d in count(4):
        b, c = 2**d - 1, 2**(d-1)
        for i, j in combinations(range(1, d-1), 2):
            yield int(bin(b - (c >> i) - (c >> j))[2:])
print(list(islice(agen(), 30))) # Michael S. Branicky, Oct 19 2022
(Python)
from itertools import count, islice
def A357774_gen(): # generator of terms
    for l in count(2):
        m = (10**(l+2)-1)//9
        for i in range(l, 0, -1):
            k = m-10**i
            yield from (k-10**j for j in range(i-1, 0, -1))
A357774_list = list(islice(A357774_gen(), 30)) # Chai Wah Wu, Feb 19 2023
(PARI) isok(k) = (k%2) && (#binary(k) == hammingweight(k)+2); \\ A357773
f(n) = fromdigits(binary(n), 10); \\ A007088
lista(nn) = apply(f, select(isok, [1..nn])); \\ Michel Marcus, Oct 19 2022

Crossrefs

Cf. A000217, A007088, A357773.

A267524 \ {1, 10, 100} and A267705 \ {1, 10} are two subsequences.

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

Sequence in context: A130600 A328947 A114387 * A204965 A192776 A218640

Adjacent sequences: A357771 A357772 A357773 * A357775 A357776 A357777

Keyword

nonn,base

Author

Bernard Schott, Oct 19 2022

Status

approved