A337833 - OEIS

A337833

Minimum m coprime to 5 such that the convergence speed of m^^m := m^(m^^(m-1)) is equal to n >= 0, where A317905(n) represents the convergence speed of m^^m (and m = A047201(n), the n-th non-multiple of 5).

1, 2, 7, 57, 182, 3124, 1068, 32318, 390624, 280182, 3626068, 23157318, 120813568, 1220703124, 1097376068, 11109655182, 49925501068, 762939453124, 355101282318, 19073486328124, 15613890344818, 365855836217682, 2384185791015624

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OFFSET

0,2

COMMENTS

Let "s" denote the last digit of m, and V(m(s)) its convergence speed. For any n, the smallest bases that are not congruent to 5 modulo 10 (as in A337392) cannot be such that s = 6, since V(m(6)) = V(m(4)) + 2.

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=0..22.

Marco Ripà, On the constant congruence speed of tetration, Notes on Number Theory and Discrete Mathematics, 2020, 26(3), 245-260.

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

EXAMPLE

For n = 19, a(19) = 19073486328124 is the smallest base (radix-10) of the tetration m^^m which is characterized by a congruence speed of 19.

CROSSREFS

Cf. A317824, A317903, A317905, A321130, A337392.

Sequence in context: A034939 A048898 A034935 * A294948 A178769 A121079

Adjacent sequences: A337830 A337831 A337832 * A337834 A337835 A337836

KEYWORD

nonn,base

AUTHOR

Marco Ripà, Sep 24 2020

STATUS

approved