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).

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

0,2

Comments

OFF cells outside the triangle of active cells are ignored.

Links

Table of n, a(n) for n=0..43.

Rémy Sigrist, C program for A319606

Example

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]

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

Prog

(C) See Links section.

Crossrefs

Cf. A317530.

Sequence in context: A024821 A059610 A341783 * A230239 A194154 A297291

Adjacent sequences: A319603 A319604 A319605 * A319607 A319608 A319609

Keyword

nonn

Author

Philipp O. Tsvetkov, Sep 24 2018

Extensions

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

Status

approved