| Autor: |
Brier, Éric, Géraud-Stewart, Rémi, Naccache, David, Pacco, Alessandro, Troiani, Emanuele |
| Rok vydání: |
2020 |
| Předmět: |
|
| Druh dokumentu: |
Working Paper |
| Popis: |
In this paper we consider a variant of Conway's sequence (OEIS A005150, A006715) defined as follows: the next term in the sequence is obtained by considering contiguous runs of digits, and rewriting them as $ab$ where $b$ is the digit and $a$ is the maximum of $b$ and the run's length. We dub this the "look-and-say the biggest" (LSB) sequence. Conway's sequence is very similar ($b$ is just the run's length). For any starting value except 22, Conway's sequence grows exponentially: the ration of lengths converges to a known constant $\lambda$. We show that LSB does not: for every starting value, LSB eventually reaches a cycle. Furthermore, all cycles have a period of at most 9. |
| Databáze: |
arXiv |
| Externí odkaz: |
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