Consider the infinite product , and write this as . Relate to the binary expression of . The sequence starts off as: .

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# q-Powerseries and binary strings

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Consider the infinite product , and write this as . Relate to the binary expression of . The sequence starts off as: .

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The sequence is exactly the sum of 1s appearing in the binary expression of (one needs not to be a root of unity in order for to be well-defined).

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