A389365 - OEIS

A389365

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

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

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OFFSET

2,1

COMMENTS

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

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..73.

Marco Ripà, The congruence speed formula, Notes on Number Theory and Discrete Mathematics, 2021, 27(4), 43-61.

Marco Ripà and Gabriele Di Pietro, A Compact Notation for Peculiar Properties Characterizing Integer Tetration, Zenodo, 2025.

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

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

EXAMPLE

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.

CROSSREFS

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

Sequence in context: A383717 A056552 A049273 * A053590 A208644 A162323

Adjacent sequences: A389362 A389363 A389364 * A389366 A389367 A389368

KEYWORD

nonn,hard

AUTHOR

Marco Ripà and Gabriele Di Pietro, Dec 09 2025

STATUS

approved