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

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