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A385893 Cycle of length 130 in the dynamical system A385938 starting from 26.

%I A385893 #27 Jul 17 2025 20:13:35
%S A385893 26,61,41,96,64,43,29,68,159,106,71,166,111,74,173,404,943,629,1468,
%T A385893 979,653,1524,1016,2371,1581,1054,703,469,313,209,488,1139,2658,1772,
%U A385893 4135,2757,1838,4289,10008,6672,4448,10379,24218,56509,37673,87904,58603,39069,26046,17364
%N A385893 Cycle of length 130 in the dynamical system A385938 starting from 26.
%C A385893 Starting from 26, iteration of A385938 returns to 26 after exactly 130 steps.
%C A385893 The dynamical system has four attractors: fixed point 1, and cycles of lengths 10, 68, and 130.
%C A385893 Any element in this cycle generates the complete 130-elements cycle when iterated.
%H A385893 Miquel Cerda, <a href="/A385893/b385893.txt">Table of n, a(n) for n = 0..129</a>
%F A385893 a(0) = 26; a(n) = A385938(a(n-1)) for n >= 1.
%e A385893 Starting from 26: f(26) = (7*26+1)/3 = 61, f(61) = (2*61+1)/3 = 41, continuing this process yields the 130-element cycle.
%t A385893 f[x_] := Which[Mod[x, 3] == 0, 2*x/3, Mod[x, 3] == 1, (2*x + 1)/3, Mod[x, 3] == 2, (7*x + 1)/3]; NestList[f, 26, 129]
%o A385893 (PARI) my(v=vector(130)); v[1]=26; for(i=2,130, x=v[i-1]; v[i]=if(x%3==0,2*x/3,if(x%3==1,(2*x+1)/3,(7*x+1)/3))); v;
%Y A385893 Cf. A385938 (the function defining this dynamical system).
%K A385893 nonn,easy,fini,full
%O A385893 0,1
%A A385893 _Miquel Cerda_, Jul 12 2025