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Results tagged with digits
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user 4312
4
votes
Does this sequence of ratios of digit sums have a limit?
If the limit exists, it of course equals 1. Indeed, $A(m):=a(m)a(m+1)\dots a(2m-1)=ds_{10}(3^m)/ds_{10}(3^{2m})\in [\frac1{9m},9m]$. But if $\lim a(m)\ne 1$, then $A(m)$ is either exponentially large …
- 109k
4
votes
Accepted
Runs of consecutive numbers that are not relatively prime to their digital sum
Let $s(n)$ denote the sum of decimal digits of $n$.
Lemma. …
- 109k