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Update 2017.08.28: I am still looking for references. I have posted a request to https://cs.stackexchange.com/q/79971 which includes some literature references I found which are of interest but still ...

Edit 2018.08.08 This answer https://mathoverflow.net/a/307881 will be updated to give recent information about S, especially a forthcoming preprint. End Edit 2018.08.08 In an introductory post on ...

This is likely piling one mystery on another, but ... I was exploring a function $f(n): \mathbb{N} \mapsto \mathbb{N}$ defined as follows: $$ f(n) = \begin{cases} n^2 & \text{if} \;n \;\text{is ...

Consider the function $f$ on the prime numbers defined by $$ f(p):= \text{ the greatest prime factor of } 2p+1.$$ The iteration of $f$ from any prime $p<10^8$ converges to the cycle $$(3,7,5,11,23,...

Let $n$ be a natural number whose prime factorization is $$n=\prod_{i=1}^{k}p_i^{\alpha_i} \; .$$ Define a function $g(n)$ as follows $$g(n)=\sum_{i=1}^{k}p_i {\alpha_i} \;,$$ i.e., exponentiation is "...

@JosephO'Rourke asked a question about a Collatz like function related to primes: $f(n) = \begin{cases} n^2 & \text{if} \;n \;\text{is prime} \\ \lfloor n/2 \rfloor & \text{if} \;n \;\text{...