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A352196
a(n) = number of steps for the mod-n Ackermann function to stabilize to a set consisting of only one value, or -1 if it does not stabilize.
1
0, 2, 4, 3, 5, 4, 6, 3, 6, 5, 6, 4, 6, 4, 4, 4, 6, 4, 7, 4, 4, 5, 6, 4, 8, 4, 6, 4, 7, 4, 6, 5, 7, 6, 4, 4, 7, 6, 4, 4, 7, 4, 5, 5, 4, 5, 6, 4, 6, 5, 5, 4, 9, 5, 8, 4, 6, 6, 6, 4, 7, 5, 4, 5, 4, 5, 8, 5, 8, 4, 7, 4, 6, 6, 7, 6, 7, 4, 7, 4, 9, 6, 8, 4, 5, 5, 7, 5, 9, 4, 4, 5, 5, 5, 6, 5, 5, 6, 6, 5, 8, 5, 7, 4, 4, 6, 5, 5, 8, 6, 7, 4, 8, 5, 7, 5, 4, 7, 6
OFFSET
1,2
COMMENTS
This was Stan Wagon's Problem of the Week #1340, from March 2022, which in turn was based on a 1993 Monthly problem of Jon Froemke and Jerrold Grossman.
Stan Wagon mentions that Mark Rickert has found the first 8 million terms (see link), and the only one that does not stabilize is n = 1969 where it becomes periodic with period 2 after 8 steps. So a(1969) = -1.
LINKS
Jon Froemke and Jerrold W. Grossman, A Mod-n Ackermann Function, or What's So Special About 1969?, The American Mathematical Monthly, Vol. 100, No. 2 (February 1993), pp. 180-183; ResearchGate link.
Mark Rickert, The first 8 million terms a(n) [a gzipped file], March 2022.
CROSSREFS
Sequence in context: A163984 A283366 A048186 * A060762 A371924 A328793
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Mar 23 2022
STATUS
approved