A Fast-Growing Sequence Inspired by TREE(k)

Inspired by the tree sequence, a novel sequence of tuples is constructed. The maximum length of such a sequence is studied and it turns out the sequence grows very fast. It is remarkable to see how our results can be expressed using Knuth’s up-arrow notation and the recursive Ackermann function, and...

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Bibliographic Details
Published in:The College mathematics journal 2020-01, Vol.51 (1), p.43-50
Main Author: Du, Kevin Y.
Format: Article
Language:English
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Summary:Inspired by the tree sequence, a novel sequence of tuples is constructed. The maximum length of such a sequence is studied and it turns out the sequence grows very fast. It is remarkable to see how our results can be expressed using Knuth’s up-arrow notation and the recursive Ackermann function, and that it is associated with Eulerian numbers.
ISSN:0746-8342
1931-1346
DOI:10.1080/07468342.2020.1680227