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.

Showing 1-8 of 8 results.

A085587 Eventual period of a single cell in rule 90 cellular automaton in a cyclic universe of width n.

Original entry on oeis.org

1, 1, 1, 1, 3, 2, 7, 1, 7, 6, 31, 4, 63, 14, 15, 1, 15, 14, 511, 12, 63, 62, 2047, 8, 1023, 126, 511, 28, 16383, 30, 31, 1, 31, 30, 4095, 28, 87381, 1022, 4095, 24, 1023, 126, 127, 124, 4095, 4094, 8388607, 16, 2097151, 2046, 255, 252, 67108863, 1022, 1048575, 56, 511, 32766, 536870911, 60
Offset: 1

Views

Author

N. J. A. Sloane, Jul 03 2003

Keywords

Links

  • O. Martin, A. M. Odlyzko, S. Wolfram, Algebraic properties of cellular automata, Comm. Math. Physics, 93 (1984), pp. 219-258, Reprinted in Theory and Applications of Cellular Automata, S. Wolfram, Ed., World Scientific, 1986, pp. 51-90 and in Cellular Automata and Complexity: Collected Papers of Stephen Wolfram, Addison-Wesley, 1994, pp. 71-113. See Table 1.
  • S. Wolfram, Statistical mechanics of cellular automata, Rev. Mod. Phys., 55 (1983), 601-644. (See Section 4.) [Added by _N. J. A. Sloane_, Apr 20 2010]

Crossrefs

Cf. A085588, A085589, A085590, A085591, A085592, A085593, A085595.
Cf. also A180001, A334496, A334499-A334515.

Extensions

More terms from Sean A. Irvine, Jun 10 2018
Definition edited by N. J. A. Sloane, May 05 2020

A085588 Eventual period of a single cell in rule 150 cellular automaton in a cyclic universe of width n.

Original entry on oeis.org

1, 2, 3, 1, 7, 4, 7, 6, 31, 2, 21, 14, 15, 8, 15, 14, 511, 12, 63, 62, 2047, 4, 1023, 42, 511, 28, 16383, 30, 31, 16, 31, 30, 4095, 28, 29127, 1022, 4095, 24, 1023, 126, 127, 124, 4095, 4094, 8388607, 8, 2097151, 2046, 255, 84, 67108863, 1022, 1048575, 56, 511, 32766, 536870911, 60, 17043521, 62, 63, 32, 63, 62
Offset: 3

Views

Author

N. J. A. Sloane, Jul 03 2003

Keywords

Comments

From Roman Khrabrov, Aug 17 2024: (Start)
It appears that 2^A007814(n) * (2^A309786(n) - 1) divides a(n). For rule 90, it follows from Lemma 3.5 and Theorem 3.5 from Martin & Odlyzko & Wolfram's paper, and the definition of A309786. Rule 150 appears to have the same behavior (verified for n <= 1000).
The numbers for which a(n) differs from 2^A007814(n) * (2^A309786(n) - 1), are the powers of 2 and the numbers in the form 6*2^k, 13*2^k, 37*2^k, 61*2^k, 67*2^k, 95*2^k and so on (there is no corresponding OEIS sequence).
It seems that in 2D case (totalistic rule 34 on a toroidal grid) the formula 2^A007814(n) * (2^A309786(n) - 1) gives the correct maximum cycle lengths in all cases except powers of 2. Replacing A007814(n) with A091090(n) appears to always provide the correct maximum cycle lengths, even at powers of 2.
Conjecture: a(n) = n only if n belongs to A115770. The inverse does not hold true in general; the first exception is 445. (End)

References

  • O. Martin, A. M. Odlyzko and S. Wolfram, Algebraic properties of cellular automata, Comm Math. Physics, 93 (1984), pp. 219-258, Reprinted in Theory and Applications of Cellular Automata, S Wolfram, Ed., World Scientific, 1986, pp. 51-90 and in Cellular Automata and Complexity: Collected Papers of Stephen Wolfram, Addison-Wesley, 1994, pp. 71-113 See Table 1.

Links

Crossrefs

Cf. A085587-A085595.

Extensions

More terms from Sean A. Irvine, Jun 10 2018
Name clarified by Roman Khrabrov, Aug 17 2024

A085593 Maximal cycle lengths in a certain class of one-dimensional cellular automata.

Original entry on oeis.org

2, 4, 6, 2, 14, 8, 14, 12, 62, 4, 42, 28, 30, 16, 30, 28, 1022, 24, 126, 124, 4094, 8, 2046, 84, 1022, 56, 32766, 60, 62, 32, 62, 60, 8190, 56, 58254, 2044, 8190, 48
Offset: 3

Views

Author

N. J. A. Sloane, Jul 03 2003

Keywords

References

  • O. Martin, A. M. Odlyzko and S. Wolfram, Algebraic properties of cellular automata, Comm Math. Physics, 93 (1984), pp. 219-258, Reprinted in Theory and Applications of Cellular Automata, S Wolfram, Ed., World Scientific, 1986, pp. 51-90 and in Cellular Automata and Complexity: Collected Papers of Stephen Wolfram, Addison-Wesley, 1994, pp. 71-113 See Table 1.

Crossrefs

Cf. A085587-A085595.

A085589 Maximal cycle lengths in a certain class of one-dimensional cellular automata.

Original entry on oeis.org

6, 2, 8, 6, 26, 4, 18, 8, 242, 6, 26, 26, 24, 16, 1640, 18, 19682, 16, 78, 242, 177146, 12, 59048, 26, 54, 26, 4782968, 24, 1103762, 160, 726, 1640, 265720, 18, 19682, 19682, 78, 80, 80, 78, 804642554, 484, 72, 177146, 94143178826, 48, 10460353202, 59048, 4920, 52
Offset: 3

Views

Author

N. J. A. Sloane, Jul 03 2003

Keywords

References

  • O. Martin, A. M. Odlyzko and S. Wolfram, Algebraic properties of cellular automata, Comm Math. Physics, 93 (1984), pp. 219-258, Reprinted in Theory and Applications of Cellular Automata, S Wolfram, Ed., World Scientific, 1986, pp. 51-90 and in Cellular Automata and Complexity: Collected Papers of Stephen Wolfram, Addison-Wesley, 1994, pp. 71-113 See Table 1.

Crossrefs

Cf. A085587-A085595.

Extensions

More terms from Sean A. Irvine, Jun 15 2018

A085590 Maximal cycle lengths in a certain class of one-dimensional cellular automata.

Original entry on oeis.org

1, 2, 8, 6, 26, 8, 1, 8, 121, 6, 13, 26, 24, 80, 6560, 18, 19682, 40, 78, 242, 88573, 24, 59048, 26, 1, 26, 4782968, 24, 14348906, 6560, 363, 6560, 265720, 18, 19682, 19682, 39, 40, 80, 78, 10460353202, 14762, 72, 177146, 47071589413, 240, 10460353202, 59048, 19680, 364
Offset: 3

Views

Author

N. J. A. Sloane, Jul 03 2003

Keywords

References

  • O. Martin, A. M. Odlyzko and S. Wolfram, Algebraic properties of cellular automata, Comm Math. Physics, 93 (1984), pp. 219-258, Reprinted in Theory and Applications of Cellular Automata, S Wolfram, Ed., World Scientific, 1986, pp. 51-90 and in Cellular Automata and Complexity: Collected Papers of Stephen Wolfram, Addison-Wesley, 1994, pp. 71-113 See Table 1.

Crossrefs

Cf. A085587-A085595.

Extensions

More terms from Sean A. Irvine, Jun 15 2018

A085591 Maximal cycle lengths in a certain class of one-dimensional cellular automata.

Original entry on oeis.org

3, 2, 4, 3, 13, 8, 9, 8, 121, 6, 13, 13, 12, 80, 820, 9, 9841, 40, 39, 242, 88573, 24, 29524, 26, 27, 26, 2391484, 24, 551881, 6560, 363, 6560, 132860, 18, 9841, 9841, 39, 40
Offset: 3

Views

Author

N. J. A. Sloane, Jul 03 2003

Keywords

References

  • O. Martin, A. M. Odlyzko and S. Wolfram, Algebraic properties of cellular automata, Comm Math. Physics, 93 (1984), pp. 219-258, Reprinted in Theory and Applications of Cellular Automata, S Wolfram, Ed., World Scientific, 1986, pp. 51-90 and in Cellular Automata and Complexity: Collected Papers of Stephen Wolfram, Addison-Wesley, 1994, pp. 71-113 See Table 1.

Crossrefs

Cf. A085587-A085595.

A085592 Maximal cycle lengths in a certain class of one-dimensional cellular automata.

Original entry on oeis.org

2, 1, 6, 2, 14, 1, 14, 6, 62, 4, 126, 14, 30, 1, 30, 14, 1022, 12, 126, 62, 4094, 8, 2046, 126, 1022, 28, 32766, 30, 62, 1, 62, 30, 8190, 28, 174762, 1022, 8190, 24
Offset: 3

Views

Author

N. J. A. Sloane, Jul 03 2003

Keywords

References

  • O. Martin, A. M. Odlyzko and S. Wolfram, Algebraic properties of cellular automata, Comm Math. Physics, 93 (1984), pp. 219-258, Reprinted in Theory and Applications of Cellular Automata, S Wolfram, Ed., World Scientific, 1986, pp. 51-90 and in Cellular Automata and Complexity: Collected Papers of Stephen Wolfram, Addison-Wesley, 1994, pp. 71-113 See Table 1.

Crossrefs

Cf. A085587-A085595.

A085596 Cycle lengths in a certain class of one-dimensional cellular automata.

Original entry on oeis.org

6, 6, 15, 12, 9, 12, 42, 30, 93, 24, 63, 18, 510, 24, 255, 84, 513, 60, 1170, 186, 6141, 48, 3075, 126, 3066, 36, 9831, 1020
Offset: 3

Views

Author

N. J. A. Sloane, Jul 03 2003

Keywords

References

  • O. Martin, A. M. Odlyzko and S. Wolfram, Algebraic properties of cellular automata, Comm Math. Physics, 93 (1984), pp. 219-258, Reprinted in Theory and Applications of Cellular Automata, S Wolfram, Ed., World Scientific, 1986, pp. 51-90 and in Cellular Automata and Complexity: Collected Papers of Stephen Wolfram, Addison-Wesley, 1994, pp. 71-113 See page 245.

Crossrefs

Cf. A085587-A085595.
Showing 1-8 of 8 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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