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

26, 61, 41, 96, 64, 43, 29, 68, 159, 106, 71, 166, 111, 74, 173, 404, 943, 629, 1468, 979, 653, 1524, 1016, 2371, 1581, 1054, 703, 469, 313, 209, 488, 1139, 2658, 1772, 4135, 2757, 1838, 4289, 10008, 6672, 4448, 10379, 24218, 56509, 37673, 87904, 58603, 39069, 26046, 17364

Offset

0,1

Comments

Starting from 26, iteration of A385938 returns to 26 after exactly 130 steps.

The dynamical system has four attractors: fixed point 1, and cycles of lengths 10, 68, and 130.

Any element in this cycle generates the complete 130-elements cycle when iterated.

Links

Miquel Cerda, Table of n, a(n) for n = 0..129

Formula

a(0) = 26; a(n) = A385938(a(n-1)) for n >= 1.

Example

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.

Mathematica

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]

Prog

(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;

Crossrefs

Cf. A385938 (the function defining this dynamical system).

Sequence in context: A277976 A291105 A267294 * A162316 A173085 A044128

Adjacent sequences: A385890 A385891 A385892 * A385894 A385895 A385896

Keyword

nonn,easy,fini,full

Author

Miquel Cerda, Jul 12 2025

Status

approved