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

1,3

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

Table of n, a(n) for n=1..7.

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

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.

Crossrefs

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

Sequence in context: A314363 A031069 A314364 * A320381 A309292 A050851

Adjacent sequences: A321127 A321128 A321129 * A321131 A321132 A321133

Keyword

nonn,fini,full

Author

Marco Ripà, Oct 27 2018

Status

approved