|
|
A356946
|
|
Number of stable digits of the integer tetration n^^n (i.e., maximum nonnegative integer m such that n^^n is congruent modulo 10^m to n^^(n + 1)).
|
|
0
|
|
|
|
OFFSET
|
1,3
|
|
COMMENTS
|
a(10) = 10^^9 is too large to include. In general, if n is a multiple of 10, then a(n) is given by the number of trailing zeros that appear at the end of n^^n.
This follows from the constancy of the "congruence speed" (AKA "convergence speed" here on the OEIS) of hyper-3 for any exponentiation base which is a multiple of 10, otherwise the congruence speed is constant only for hyper-4 and it is strictly positive for any tetration base n >= 1 that is not a multiple of 10 (for an explicit formula to calculate a(n) for any n, see the linked paper entitled "Number of stable digits of any integer tetration").
|
|
REFERENCES
|
Marco Ripà, La strana coda della serie n^n^...^n, Trento, UNI Service, Nov 2011. ISBN 978-88-6178-789-6.
|
|
LINKS
|
|
|
EXAMPLE
|
For n = 3, 3^3^3 is congruent to 3^3^3^3 (mod 10^2) and 3^3^3 is not congruent to 3^3^3^3 (mod 10^3). Thus, a(3) = 2.
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,base
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|