Answer by Richard Stanley for Are there results in "Digit Theory"?
James Maynard has a survey paper Digits of primes. In Primes with restricted digits he shows that for any digit $d\in\{0,1,\dotsc,9\}$ there are infinitely many primes that do not have $d$ in their...
View ArticleAnswer by AfterMath for Are there results in "Digit Theory"?
It may or may not be results of the type you are looking for, but one have deduced asymptotic formulae for the average value of the digit sum $S_b(n)$ considered a function of $n$ and considered a...
View ArticleAnswer by user6976 for Are there results in "Digit Theory"?
I "discovered" this theory 40 years ago (I was 16 years old). In particular, I found the formula that you attribute to Kurt Hensel in a paper by Bunjakovskiĭ published in 188... (this might be the...
View ArticleAnswer by darij grinberg for Are there results in "Digit Theory"?
Persi Diaconis gave a talk about probabilities of carries at MIT about half a year ago. Unfortunately I was so busy trying to spot symmetric functions in the talk that most of it drifted past my mind,...
View ArticleAnswer by Woett for Are there results in "Digit Theory"?
Benford's Law is quite a famous example, I guess. Although at first this was just an 'empirical law', there are actually good mathematical reasons for its existence. And, for example, the Fibonacci...
View ArticleAnswer by KConrad for Are there results in "Digit Theory"?
Lucas proved a congruence for binomial coefficients mod a prime $p$ that uses the base $p$ digits of the two numbers in the binomial coefficient. See http://en.wikipedia.org/wiki/Lucas%27_theorem. It...
View ArticleAnswer by Salvo Tringali for Are there results in "Digit Theory"?
I don't know if the following qualifies as an "interesting result" in "digit theory", but Carlo Sanna, a student from the Università di Torino, has recently published a paper in elementary number...
View ArticleAre there results in "Digit Theory"?
Results about numbers that are related to their decimal representation are usually confined to recreational mathematics. There I have seen mainly questions about individual numbers, like finding a...
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