设正整数 n = a 0 ⋅ 2 0 + a 1 ⋅ 2 1 + a 2 ⋅ 2 2 ⋯ + a k - 1 ⋅ 2 k - 1 + a k ⋅ 2 k ,其中 a i ∈ 0 , 1 ,记 ω n = a 0 + a 1 + ⋯ + a k .则( )
ω 2 n = ω n
ω 2 n + 3 = ω n + 1
ω 8 n + 5 = ω 4 n + 3
ω 2 n - 1 = n
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