A352196 a(n) = number of steps for the standard 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

Author

N. J. A. Sloane, Mar 23 2022

Keywords

• nonn

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.

[Needs program(s), b-file. - N. J. A. Sloane, May 25 2025]

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 of A085119 [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

Cf. A085119.

Extensions

"Standard" added to definition by N. J. A. Sloane, May 25 2025 to be consistent with the Froemke-Grossman (1993) article.