A321131 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.

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

Offset

2,1

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 unitary convergence speed.

64% 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=2..17.

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

Example

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

Crossrefs

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

Sequence in context: A138394 A140752 A246780 * A191983 A055562 A235933

Adjacent sequences: A321128 A321129 A321130 * A321132 A321133 A321134

Keyword

nonn,fini,full

Author

Marco Ripà, Oct 27 2018

Status

approved