OFFSET
2,5
COMMENTS
If b>=2 and a>=b^3 then E(a,2,b)<a. For each positive integer a, there is an positive integer m such that E^m(a,2,b)<b^3. (Fox et al., 2024, Lemma 4).
LINKS
Nathan Fox, Table of n, a(n) for n = 2..100
N. Bradley Fox et al., Elated Numbers, arXiv:2409.09863 [math.NT], 2024.
EXAMPLE
In the decimal system all integers go to (1), (298), (46, 208, 136), (26, 80, 512, 150), or (33, 54, 205, 58, 445, 228, 144) under iteration of the map A376270, hence there are two fixed points and three cycles. Therefore a(10) = 3.
CROSSREFS
KEYWORD
nonn,base
AUTHOR
N. Bradley Fox, Nathan Fox, Helen Grundman, Rachel Lynn, Changningphaabi Namoijam, Mary Vanderschoot, Oct 15 2024
STATUS
approved