A354959 Tetration bases with a constant convergence speed >= 3.

15, 25, 55, 57, 65, 68, 95, 105, 124, 126, 135, 145, 175, 182, 185, 193, 215, 225, 249, 255, 265, 295, 305, 318, 335, 345, 374, 375, 376, 385, 415, 425, 432, 455, 465, 495, 505, 535, 545, 568, 575, 585, 615, 624, 625, 626, 655, 665, 682, 695, 705, 735, 745

Offset

1,1

Comments

The convergence speed of any integer greater than 1 and not divisible by 10 is constant if and only if we are considering an integer tetration and its constant convergence speed is greater than 2 if and only if the tetration base is of the form m + k*1000, for k >= 0, where m is a term.

Links

Marco Ripà, Table of n, a(n) for n = 1..10000

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

57 is a term since the constant convergence speed of 57 is 3 and (trivially) 57 has no trailing zeros.

Crossrefs

Cf. A317905, A337392, A337833, A321130, A321131.

Sequence in context: A031888 A299469 A046291 * A280406 A020302 A020202

Adjacent sequences: A354956 A354957 A354958 * A354960 A354961 A354962

Keyword

nonn,base

Author

Marco Ripà, Jul 23 2022

Status

approved