Number Theory

    

Number of Stable Digits of Any Integer Tetration

Authors: Marco Ripà, Luca Onnis

In the present paper we provide a general formula which let us easily calculate the number of stable digits of any integer tetration base a∈ℕU{0}. The number of stable digits, at the given height of the power tower, indicates how many of the last digits of the (generic) tetration are frozen. Our formula is exact for any tetration base which is not coprime to 10, although a maximum gap equal to V(a) + 1 digits (where V(a) indicates the congruence speed of a) can occur, in the worst-case scenario, between the given upper and lower bound.

Comments: 7 Pages.

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Submission history

[v1] 2021-12-31 00:14:30

Unique-IP document downloads: 282 times

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