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.

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

Table of n, a(n) for n=1..119.

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.

Stan Wagon, Problem of the Week POW #1340: Modular Ackermann, March 2022.

Stan Wagon, Problem of the Week POW #1340: Solution, March 2022.

Crossrefs

Sequence in context: A163984 A283366 A048186 * A060762 A371924 A328793

Adjacent sequences: A352193 A352194 A352195 * A352197 A352198 A352199

Keyword

nonn

Author

N. J. A. Sloane, Mar 23 2022

Status

approved