login
Binary expansions of odd numbers with three zeros in their binary expansion.
1

%I #25 Feb 22 2023 08:08:07

%S 10001,100011,100101,101001,110001,1000111,1001011,1001101,1010011,

%T 1010101,1011001,1100011,1100101,1101001,1110001,10001111,10010111,

%U 10011011,10011101,10100111,10101011,10101101,10110011,10110101,10111001,11000111,11001011,11001101,11010011,11010101,11011001,11100011

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

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

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

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

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

%o (Python)

%o from itertools import count, islice

%o from sympy.utilities.iterables import multiset_permutations

%o def A360574_gen(): # generator of terms

%o yield from (int('1'+''.join(d)+'1') for l in count(0) for d in multiset_permutations('000'+'1'*l))

%o A360574_list = list(islice(A360574_gen(),30)) # _Chai Wah Wu_, Feb 18 2023

%Y Cf. A000292, A007088, A360573.

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

%K nonn,base

%O 1,1

%A _Bernard Schott_, Feb 18 2023