cp's OEIS Frontend

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.

%I A133144 #12 Apr 01 2023 11:35:42
%S A133144 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,
%T A133144 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,
%U A133144 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
%N 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.
%C A133144 It is conjectured that every number eventually reaches a fixed point (see A131571) or the cycle of length 2 given by (175 <-> 78125).
%H A133144 Eder Vanzei, <a href="/A133144/b133144.txt">Table of n, a(n) for n = 0..10000</a>
%e A133144 n, a(n), trajectory
%e A133144 22, 1, [22, 4]
%e A133144 23, 1, [23, 9]
%e A133144 24, 2, [24, 16, 6]
%e A133144 25, 0, [25]
%e A133144 26, 4, [26, 36, 216, 12, 2]
%e A133144 27, 6, [27, 49, 6561, 15625, 194400, 2304, 9]
%e A133144 28, 3, [28, 64, 4096, 0]
%e A133144 29, 2, [29, 81, 1]
%e A133144 30, 1, [30, 3]
%e A133144 31, 1, [31, 1]
%e A133144 32, 1, [32, 8]
%e A133144 33, 7, [33, 27, 49, 6561, 15625, 194400, 2304, 9]
%e A133144 34, 3, [34, 64, 4096, 0]
%e A133144 35, 2, [35, 125, 25]
%e A133144 36, 3, [36, 216, 12, 2]
%e A133144 37, 6, [37, 343, 243, 162, 64, 4096, 0]
%e A133144 38, 3, [38, 512, 10, 1]
%e A133144 39, 7, [39, 729, 567, 588245, 5242880000, 8589934592, 105911076180375000000000, 0]
%K A133144 nonn,base
%O A133144 0,25
%A A133144 _J. H. Conway_ and _N. J. A. Sloane_, Jan 01 2008