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# of 0's in decimal expansion, summation converges

Source: VJIMC 1997 1.4-M

September 30, 2021
limitsreal analysisnumber theoryDigits

Problem Statement

Find all real numbers a>0a>0 for which the series ∑n=1∞af(n)n2\sum_{n=1}^\infty\frac{a^{f(n)}}{n^2}is convergent; f(n)f(n) denotes the number of 00's in the decimal expansion of ff.
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