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s(2^n) > s(2^{n+1})

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January 17, 2015
logarithmsmodular arithmeticnumber theory unsolvednumber theory

Problem Statement

For a positive integer kk, let s(k)s(k) denote the sum of the digits of kk. Show that there are infinitely many natural numbers nn such that s(2n)>s(2n+1)s(2^n) > s(2^{n+1}).
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