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
Crossrefs
Programs
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Mathematica
FromDigits[IntegerDigits[#, 2]] & /@ Select[Range[1, 250, 2], DigitCount[#, 2, 0] == 2 &] (* Amiram Eldar, Oct 19 2022 *)
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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
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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
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Python
from math import isqrt, comb from sympy import integer_nthroot def A357774(n): a = (m:=integer_nthroot(6*n, 3)[0])+(n>comb(m+2,3))+3 b = isqrt((j:=comb(a-1,3)-n+1)<<3)+3>>1 c = j-comb((r:=isqrt(w:=j<<1))+(w>r*(r+1)),2) return (10**a-1)//9-10**b-10**c # Chai Wah Wu, Dec 19 2024
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