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Values of m (mod 25), where A317905(m) = 1. Values of m (mod 25) such that V(m) = 1, where V(m) indicates the constant convergence speed of the tetration base m.
4

%I #24 Aug 23 2022 09:54:35

%S 2,3,4,6,8,9,11,12,13,14,16,17,19,21,22,23

%N Values of m (mod 25), where A317905(m) = 1. Values of m (mod 25) such that V(m) = 1, where V(m) indicates the constant convergence speed of the tetration base m.

%C This sequence represents the values of the base a such that a^^m, where ^^ indicates tetration or hyper-4 (e.g., 3^^4=3^(3^(3^3))), is characterized by a unitary convergence speed.

%C 64% of the positive integers belong to this list (see A317905).

%D Marco Ripà, La strana coda della serie n^n^...^n, Trento, UNI Service, Nov 2011. ISBN 978-88-6178-789-6

%H Marco Ripà, <a href="https://doi.org/10.7546/nntdm.2020.26.3.245-260">On the constant congruence speed of tetration</a>, Notes on Number Theory and Discrete Mathematics, Volume 26, 2020, Number 3, pp. 245—260.

%H Marco Ripà, <a href="https://doi.org/10.7546/nntdm.2021.27.4.43-61">The congruence speed formula</a>, Notes on Number Theory and Discrete Mathematics, 2021, 27(4), 43-61.

%H Marco Ripà and Luca Onnis, <a href="https://doi.org/10.7546/nntdm.2022.28.3.441-457">Number of stable digits of any integer tetration</a>, Notes on Number Theory and Discrete Mathematics, 2022, 28(3), 441-457.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Tetration">Tetration</a>

%e For m = 47, m (mod 25) == 22 and 22^^n has a unitary convergence speed, since A317905(m = 47) = 1 = A317905(m = 22).

%Y Cf. A067251, A317824, A317903, A317905, A321130.

%K nonn,fini,full

%O 2,1

%A _Marco Ripà_, Oct 27 2018