English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

An interesting open conjecture asks whether it is possible to walk toinfinity along primes, where each term in the sequence has one digit more thanthe previous. We present different greedy models for prime walks to predict thelong-time behavior of the trajectories of orbits, one of which has similarbehavior to the actual backtracking one. Furthermore, we study the sameconjecture for square-free numbers, which is motivated by the fact that theyhave a strictly positive density, as opposed to primes. We introduce stochasticmodels and analyze the walks' expected length and frequency of digits added.Lastly, we prove that it is impossible to walk to infinity in other importantnumber-theoretical sequences or on primes in different bases.

Walking to Infinity Along Some Number Theory sequences