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Results tagged with digits
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user 8008
2
votes
Optimal lower bounds for the sum of digits in base $b$
$ has at least $7$ non-zero digits provided that $n$ is at least $767$ (by which point $n!$ has many thousand binary digits.) … The other $12$ leading digits might be expected to split roughly equally and in fact split exactly equally. …
- 30.1k
2
votes
Does a sequence of primes defined like this exists?
I agree that the sum of the base ten digits seems rather peripheral. However: given a positive integer $M;$ let $S_M$ be the set of primes $p$ so that the base $10$ digit sum of $Mp$ is a prime. … Flimsy reasoning for why I suspect yes: Suppose $M$ has $t$ digits and consider primes with $s$ digits. …
- 30.1k
2
votes
Accepted
Partitioning integers into two parts and exploring relationships with positional numeral sys...
Here is one kind of crazy example: Start with $A,B$ any two finite sets so that all the sums $a+b$ are distinct. $A=B=\emptyset$ for example. Now consider the integers in order $0,1,-1,2,-2,\cdots$ o …
- 30.1k