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Dynamics of a curious bijection of $\mathbb N$

The two sequences A48680 and A48679 of the OEIS define two mutually inverse bijections on the set of all strictly positive natural numbers given (for the comfort of the reader) as follows: Given an ...
Roland Bacher's user avatar
3 votes
0 answers
303 views

Growth functions of finite group - computation, typical behaviour, surveys?

Looking on the growth function for Rubik's group and symmetric group, one sees rather different behaviour: Rubik's growth in LOG scale (see MO322877): S_n n=9 growth and nice fit by normal ...
Alexander Chervov's user avatar
2 votes
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266 views

Experimentation with partial Euler products

Richard Mathar $[1]\& [2]$ shows that \begin{align} &\zeta_{2}(s)\equiv\prod_{\Omega(n)=2}^{}\left(\dfrac{1}{1 - n^{s}}\right)^{-1}=\exp \left(\sum _{k=1}^n \frac{P(k s)^2+P(2 k s)}{2 k}\right)...
martin's user avatar
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1 vote
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375 views

The Knuth-Stolarsky conjecture in addition chains

I would like some general feedback on an experiment I have run in the field of addition chains. An addition chain for target integer $n$ is defined as: $$1=a_0<a_1<\cdots<a_r=n \text{ with } ...
Neill Clift's user avatar