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%I #11 Jun 09 2024 23:32:52
%S 5,7,18,24,26,32,35,43,45,49,51,74,75,76,82,85,93,99,107,115,118,125,
%T 132,143,149,151,155,157,165,168,174,176,195,199,201,205,207,218,224,
%U 226,232,235,243,245,251,257,268,274,275,276,282,285,293,299,301,307
%N Integers m whose (constant) convergence speed is exactly 2 (i.e., m^^(m+1) has 2 more rightmost frozen digits than m^^m, where ^^ indicates tetration).
%C It is well known (see Links) that as the hyperexponent of the integer m becomes sufficiently large, the constant convergence speed of m is the number of new stable digits that appear at the end of the result for any further unit increment of the hyperexponent itself, and a sufficient (but not necessary) condition to get this fixed value is to set the hyperexponent equal to m plus 1.
%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 (see Table 1, pp. 249—251).
%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 (see Equation 16, p. 454).
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Tetration">Tetration</a>
%F a(n) is such that A317905(m) = 2, for m = 5, 6, 7, ...
%e If n = 2, m = 7 and so 7^^8 has exactly 2 more stable digits at the end of the result than 7^^7.
%Y Cf. A317905 (convergence speed of m^^m), A321130, A321131, A371129.
%K nonn,base
%O 1,1
%A _Marco Ripà_, May 01 2024