# Tagged Questions

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### Prime factors of $\sum_{k=1}^{30}k^{k^k}$

I checked the prime factors of $$\sum_{k=1}^{30}k^{k^k}$$ and did not find any upto $10^8$ Are there any useful restrictions to accelerate the search ?
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### Slight confusion about the calculation of the last digits of graham's number

In Wikipedia, Graham's number, it is described how to calculate the last d digits of Graham's number. They introduce an algorithm simply iterating $$x = 3^x \mod 10^d$$ d times starting with x=3. ...
Given n, how can the number m with $10 \uparrow \uparrow m < 2 \uparrow \uparrow n < 10 \uparrow \uparrow (m+1)$ be calculated ? With induction, I got $10 \uparrow \uparrow m < 2 ... 2answers 60 views ### Recursive definition of recursively defined operations The recursive definitions of addition, multiplication, and exponentiation usually stop after exponentiation ("${\small+}1$" to be read as "the successor of"):$x \boldsymbol{+} (y\ {\small+}1) := (x ...
A friend recently asked me if I could solve these three problems: (a) Prove that the sequence $1^1, 2^2, 3^3, \dots \pmod{3}$ in other words $\{n^n \pmod{3} \}$ is periodic, and find the length of ...