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A370775
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).
3
5, 7, 18, 24, 26, 32, 35, 43, 45, 49, 51, 74, 75, 76, 82, 85, 93, 99, 107, 115, 118, 125, 132, 143, 149, 151, 155, 157, 165, 168, 174, 176, 195, 199, 201, 205, 207, 218, 224, 226, 232, 235, 243, 245, 251, 257, 268, 274, 275, 276, 282, 285, 293, 299, 301, 307
OFFSET
1,1
COMMENTS
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.
LINKS
Marco Ripà, On the constant congruence speed of tetration, Notes on Number Theory and Discrete Mathematics, Volume 26, 2020, Number 3, Pages 245—260 (see Table 1, pp. 249—251).
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 (see Equation 16, p. 454).
Wikipedia, Tetration
FORMULA
a(n) is such that A317905(m) = 2, for m = 5, 6, 7, ...
EXAMPLE
If n = 2, m = 7 and so 7^^8 has exactly 2 more stable digits at the end of the result than 7^^7.
CROSSREFS
Cf. A317905 (convergence speed of m^^m), A321130, A321131, A371129.
Sequence in context: A345909 A214414 A153192 * A263878 A297937 A337349
KEYWORD
nonn,base
AUTHOR
Marco Ripà, May 01 2024
STATUS
approved