cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

Original entry on oeis.org

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

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Author

Miquel Cerda, Jul 12 2025

Keywords

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.

Examples

			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.
		

Crossrefs

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

Programs

  • 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]
  • 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;

Formula

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