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+--- Thread: Frozen digits in any integer tetration (/showthread.php?tid=1621)
Frozen digits in any integer tetration - marcokrt - 08/13/2022
Happy to announce that me and Luca (Luknik) have finally published the paper with the direct map of the constant congruence speed of tetration: Number of stable digits of any integer tetration
Basically, assuming radix-\( 10 \), for any base \( a \in \mathbb{N}_{0} \) which is not a multiple of \( 10 \) and considering a unitary increment of a sufficiently large hyperexponent \( b \in \mathbb{Z}^{+} \), we can find the number of new stable (i.e., previously unfrozen) digits of \( {^{b}a \) by simply taking into account the \( 2 \)-adic or the \( 5 \)-adic valuation of \( a \pm 1 \), or the \( 5 \)-adic valuation of \( a^2+1 \) (see Equation 16).
The above is my third and last paper on this fascinating and peculiar property of tetration. Everything was inspired by the intriguing open field that I started to discover thanks to the registration of this forum almost \( 11 \) years ago.
Thank you everybody, feedback is welcome!
RE: Frozen digits in any integer tetration - bo198214 - 08/13/2022
Yippee, Champaign! ?
RE: Frozen digits in any integer tetration - JmsNxn - 08/14/2022
Absolutely Beautiful, Marco! Super proud and happy for you! I'm excited to read this. It's not a problem I'm particularly interested in, but this is awesome! And yes, like Bo said, have some Champagne on me!