科研之友
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摘要
Let sq(n) denote the sum of the digits of a number n expressed in base q. We study here the ratio s(q)(n(alpha))/s(q)(n) for various values of q and alpha. In 1978, Kenneth B. Stolarsky showed that lim inf(n ->infinity) s2(n(2))/s2(n) = 0 and that lim sup(n ->infinity) s2(n(2))/s2(n) = infinity using an explicit construction. We show that for alpha = 2 and q >= 2, the above ratio can in fact be any positive rational number. We also study what happens when alpha is a rational number that is not an integer, terminating the resulting expression by using the floor function.
- 出版日期2015-3
