A377126 - OEIS

%I #27 Nov 22 2024 11:17:05

%S 1,2,4,1,4,4,4,1,-1,1,2,4,1,1,2,1,2,4,-1,4,4,4,1,1,2,4,4,4,-1,4,4,2,2,

%T 1,1,4,2,2,-1,2,4,2,4,1,4,1,1,4,-1,1,1,1,4,1,4,4,4,1,-1,4,2,4,1,1,2,2,

%U 4,4,-1,4,4,4,4,1,4,4,4,4,-1,4,4,4,4,1

%N Number of digits of A376842(n) or -1 if A376842(n) = -1.

%C For any integer n > 1 not a multiple of 10, a(n) belongs to the set {1, 2, 4}. Furthermore, if the last digit of n is 5, then A376446(n) = 5 so that a(n) = 1. Conversely, by definition, a(n) -1 if and only if n is congruent to 0 modulo 10.

%C This sequence is also equal to the number of digits of A376446(n) and -1 if A376446(n) = -1; for the values of the phase shifts at heights 2 and 3 of any tetration base n which is a multiple of 10, see A376838 and A377124 (respectively).

%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.2020.26.3.245-260">On the constant congruence speed of tetration</a>, Notes on Number Theory and Discrete Mathematics, Volume 26, 2020, Number 3, Pages 245-260.

%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 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 Marco Ripà, <a href="https://arxiv.org/abs/2411.00015">Graham's number stable digits: an exact solution</a>, arXiv:2411.00015 [math.GM], 2024.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Tetration">Tetration</a>.

%F a(n) = floor(log_(10)(A376842(n))) + 1.

%F a(n) = floor(log_(10)(A376446(n))) + 1.

%F a(n) = -1 iff A376446(n) = -1; a(n) = 1 iff 1 <= A376446(n) <= 9; a(n) = 2 iff A376446(n) = {19, 28, 37, 46, 64, 73, 82, 91}; a(n) = 4 otherwise.

%e a(4) = 4 since A376446(4) = 2486 is a 4 digit number.

%Y Cf. A317905, A372490, A373387, A376446, A376838, A376842, A377124.

%K sign,base,changed

%O 2,2

%A _Marco Ripà_, Oct 17 2024