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## Main Question or Discussion Point

I'd like to see whether weird reciprocal sums of integers in the form [tex]\sum_{x\in S}\frac{1}{x}[/tex], where S is some unconventional set of integers, converges or diverge. Does anyone know any?

For example, [tex]\sum_{x\in S}\frac{1}{x}[/tex] where S is the set of integers that, when expanded in binary, represents a valid Java program compiled on the x86 architecture. Is it convergent? Divergent?

For example, [tex]\sum_{x\in S}\frac{1}{x}[/tex] where S is the set of integers that, when expanded in binary, represents a valid Java program compiled on the x86 architecture. Is it convergent? Divergent?