Triangle of the power tower k^k^k^... (mod n) for k = 1..(n-1).
1, 1, 1, 1, 0, 3, 1, 1, 2, 1, 1, 4, 3, 4, 5, 1, 2, 6, 4, 3, 1, 1, 0, 3, 0, 5, 0, 7, 1, 7, 0, 4, 2, 0, 7, 1, 1, 6, 7, 6, 5, 6, 3, 6, 9, 1, 9, 9, 4, 1, 5, 2, 3, 5, 1, 1, 4, 3, 4, 5, 0, 7, 4, 9, 4, 11, 1, 3, 1, 9, 5, 1, 6, 1, 1, 3, 6, 1, 1, 2, 13, 4, 3, 8, 7, 8, 1
2
Each row begins with 1. The tower converges after a finite number of steps. Sequence S000439 contains the height of the exponents required for convergence.
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++]; TowerMod[m, k, n], {m, n - 1}], {n, 2, 10}]
Cf. S000439.
nonn,tabl,nice
T. D. Noe, Dec 27 2014