A133144 Start with n and repeatedly apply the powerback map of A133048. Sequence gives number of steps to the point where the next number would be one that has appeared before.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 4, 6, 3, 2, 1, 1, 1, 7, 3, 2, 3, 6, 3, 7, 1, 1, 2, 2, 4, 3, 3, 3, 2, 5, 1, 1, 2, 5, 2, 2, 6, 5, 4, 2, 1, 1, 3, 7, 2, 4, 4, 5, 4, 5, 1, 1, 4, 4, 5, 2, 3, 6, 4, 3, 1, 1, 4, 5, 3, 5, 5, 3, 4, 5, 1, 1, 3, 9, 4, 6, 2, 2, 5, 3

Offset: 0

Author

J. H. Conway and N. J. A. Sloane, Jan 01 2008

Keywords

• nonn
• base

Comments

It is conjectured that every number eventually reaches a fixed point (see A131571) or the cycle of length 2 given by (175 <-> 78125).

Examples

			n, a(n), trajectory
22, 1, [22, 4]
23, 1, [23, 9]
24, 2, [24, 16, 6]
25, 0, [25]
26, 4, [26, 36, 216, 12, 2]
27, 6, [27, 49, 6561, 15625, 194400, 2304, 9]
28, 3, [28, 64, 4096, 0]
29, 2, [29, 81, 1]
30, 1, [30, 3]
31, 1, [31, 1]
32, 1, [32, 8]
33, 7, [33, 27, 49, 6561, 15625, 194400, 2304, 9]
34, 3, [34, 64, 4096, 0]
35, 2, [35, 125, 25]
36, 3, [36, 216, 12, 2]
37, 6, [37, 343, 243, 162, 64, 4096, 0]
38, 3, [38, 512, 10, 1]
39, 7, [39, 729, 567, 588245, 5242880000, 8589934592, 105911076180375000000000, 0]
		

Links

• Eder Vanzei, Table of n, a(n) for n = 0..10000