The height of the exponents in S000438.
0, 0, 2, 0, 2, 1, 0, 3, 2, 2, 0, 2, 1, 1, 1, 0, 3, 2, 1, 2, 2, 0, 3, 1, 2, 1, 2, 1, 0, 3, 2, 1, 2, 2, 1, 2, 0, 3, 2, 2, 1, 1, 2, 2, 1, 0, 4, 3, 3, 2, 2, 3, 3, 2, 2, 0, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 0, 3, 2, 2, 1, 3, 2, 2, 2, 2, 2, 2, 0, 3, 2, 1, 2, 2, 1, 1, 2
2
Each row begins with 0 because 1^1^1^… converges after 0 exponents.
T. D. Noe, Plot of rows 2..100
T. D. Noe, Table of rows 2..100
David Bessoud and Stan Wagon, A Course in Computational Number Theory, Key College Publishing, 2000.
(Mma) Table[Table[k = 1; While[TowerMod[m, k, n] != TowerMod[m, k-1, n], k++]; k-1, {m, n - 1}], {n, 2, 10}]
Cf. S000438.
nonn,tabl
T. D. Noe, Dec 27 2014