|
|
A371671
|
|
Convergence speed of n at height 2 (i.e., A369826(n) - A371074(n)).
|
|
3
|
|
|
0, 0, 0, 0, 1, 1, 3, 2, 2, 1, 1, 9, 1, 1, 1, 1, 8, 1, 1, 0, 1, 19, 1, 0, 1, 2, 7, 5, 1, 1, 1, 29, 1, 2, 1, 1, 4, 1, 1, 0, 1, 39, 1, 0, 2, 1, 5, 2, 1, 1, 2, 49, 2, 1, 1, 1, 6, 1, 3, 0, 1, 59, 1, 0, 1, 1, 17, 2, 1, 3, 1, 69, 1, 1, 1, 2, 3, 4, 1, 0, 1, 79, 1, 0
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
-1,7
|
|
COMMENTS
|
A sufficient but not necessary condition for having a constant value of the convergence speed of a tetration base n that is not a multiple of 10 (see A317905) is that the height of the hyperexponent is greater than or equal to tilde(v(a))+2, where tilde(v(a)) := v_5(a-1) iff a == 1 (mod 5), v_5(a^2+1) iff a == {2, 3} (mod 5), v_5(a+1) iff a == 4 (mod 5), v_2(a^2-1)-1 iff a == 5 (mod 10), where v_2(x) = A007814(x) and v_5(x) = A112765(x) are the 2-adic and 5-adic valuations, respectively (see "Number of stable digits of any integer tetration", p. 447, Definition 2.1, in Links).
|
|
LINKS
|
|
|
FORMULA
|
|
|
EXAMPLE
|
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,base
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|