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.

A319606 a(n) is that generation of the rule-30 1D cellular automaton started from a single ON cell in which n successive OFF cells appears for the first time after a(n-1).

Original entry on oeis.org

1, 4, 5, 9, 11, 21, 34, 45, 51, 88, 106, 131, 137, 158, 193, 251, 517, 772, 1029, 1283, 1539, 1794, 2052, 2305, 2561, 4101, 5121, 8197, 10241, 12291, 16388, 20482, 32772, 36865, 49154, 57345, 65539, 262150, 294913, 786437, 851969, 1310724, 1441793, 1835011
Offset: 0

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Author

Philipp O. Tsvetkov, Sep 24 2018

Keywords

Comments

OFF cells outside the triangle of active cells are ignored.

Examples

			The Rule-30 1D cellular automaton started from a single ON (.) cell generates the following triangle:
1                          .
2                        . . .
3                      . . 0 0 .
4                    . . 0 . . . .
5                  . . 0 0 . 0 0 0 .
6                . . 0 . . . . 0 . . .
7              . . 0 0 . 0 0 0 0 . 0 0 .
8            . . 0 . . . . 0 0 . . . . . .
9          . . 0 0 . 0 0 0 . . . 0 0 0 0 0 .
10       . . 0 . . . . 0 . . 0 0 . 0 0 0 . . .
11     . . 0 0 . 0 0 0 0 . 0 . . . . 0 . . 0 0 .
12   . . 0 . . . . 0 0 . . 0 . 0 0 0 0 . 0 . . . .
13 . . 0 0 . 0 0 0 . . . 0 0 . . 0 0 . . 0 . 0 0 0 .
0 OFF cell appears for the first time in generation (line) 1, thus a(0) = 1;
1 consecutive OFF cells (0) appear for the first time after line 1 in generation (line) 4, thus a(1) = 4;
2 consecutive OFF cells (00) appear for the first time after (line) 4 in generation (line) 5, thus a(2) = 5. [Corrected by _Rémy Sigrist_, Jul 06 2020]
		

Crossrefs

Cf. A317530.

Programs

  • C
    See Links section.
  • Mathematica
    CellularAutomaton[30, {{1}, 0}, 20000];
    (Reverse[Internal`DeleteTrailingZeros[
          Reverse[Internal`DeleteTrailingZeros[#]]]]) & /@ %;
    ls = Table[
       Max[Differences[Position[Flatten@{1, %[[n]], 1}, 1]]] - 1, {n, 1,
        20000}];
    res = {1};
    Table[Position[ls, n] // Flatten, {n, 100}];
    For[n = 1, n < 40, n++,
    AppendTo[res, (Select[%[[n]], # > Last[res] &, 1][[1]])]]
    res

Extensions

Data corrected and more terms from Rémy Sigrist, Jul 06 2020