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%I #42 Apr 01 2022 10:58:30
%S 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,
%T 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,
%U 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
%N 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.
%C 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.
%C 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.
%H Jon Froemke and Jerrold W. Grossman, <a href="https://www.jstor.org/stable/2323780">A Mod-n Ackermann Function, or What's So Special About 1969?</a>, The American Mathematical Monthly, Vol. 100, No. 2 (February 1993), pp. 180-183; <a href="https://www.researchgate.net/publication/2795061_Ackermann_Function_or_What's_So_Special_about_1969">ResearchGate link</a>.
%H Mark Rickert, <a href="/A352196/a352196-8M.gz">The first 8 million terms a(n)</a> [a gzipped file], March 2022.
%H Stan Wagon, <a href="/A352196/a352196.pdf">Problem of the Week POW #1340: Modular Ackermann</a>, March 2022.
%H Stan Wagon, <a href="/A352196/a352196_1.pdf">Problem of the Week POW #1340: Solution</a>, March 2022.
%K nonn
%O 1,2
%A _N. J. A. Sloane_, Mar 23 2022