A389365 - OEIS

%I #27 Dec 22 2025 17:09:49

%S 2,3,2,5,6,7,2,2,10,11,6,13,14,15,2,17,2,19,7,21,22,23,3,2,26,2,7,29,

%T 30,31,2,33,34,35,2,37,38,39,3,41,42,43,9,45,46,47,3,2,2,51,23,53,2,

%U 55,3,57,58,59,30,61,62,2,2,65,66,67,34,69,70,71,2,73

%N Smallest integer > 1 whose congruence speed never stabilizes in the radix-n numeral system.

%C This sequence consists of all the terms (greater than 1) of A005117 and A390535.

%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.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 Gabriele Di Pietro, <a href="https://doi.org/10.5281/zenodo.17626007">A Compact Notation for Peculiar Properties Characterizing Integer Tetration</a>, Zenodo, 2025.

%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>.

%F If n equals the m-th non-squarefree positive integer, then a(n) = A390535(m); a(n) = n otherwise.

%e a(10) = 10 since 10 is squarefree, and thus the only integers > 1 without a constant congruence speed in radix-10 are the multiples of 10.

%Y Cf. A005117, A013929, A373387, A390535, A390598.

%K nonn,hard

%O 2,1

%A _Marco Ripà_ and _Gabriele Di Pietro_, Dec 09 2025