A321130 Values of m (mod 25) such that V(m) >= 2, where V(m) indicates the constant convergence speed of the tetration base m.

0, 1, 5, 7, 15, 18, 24

Offset: 1

Author

Marco Ripà, Oct 27 2018

Keywords

• nonn
• fini
• full

Comments

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 convergence speed at or above 2 (fast m-adic convergence). Only 26% of the positive integers belong to this list (see A317905).

References

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

Links

• Marco Ripà, On the constant congruence speed of tetration, Notes on Number Theory and Discrete Mathematics, Volume 26, 2020, Number 3, pp. 245—260.
• Marco Ripà, The congruence speed formula, Notes on Number Theory and Discrete Mathematics, 2021, 27(4), 43-61.
• Marco Ripà and Luca Onnis, Number of stable digits of any integer tetration, Notes on Number Theory and Discrete Mathematics, 2022, 28(3), 441-457.
• Wikipedia, Tetration

Crossrefs

Cf. A067251, A317824, A317903, A317905, A321131.

Formula

For m = 57, m (mod 25) == 7 and 7^^n has a convergence speed greater than 1, since A317905(m = 57) = 3 > 1 and also A317905(m = 7) = 2 > 1.