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.

A317530 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.

Original entry on oeis.org

4, 3, 5, 7, 9, 17, 45, 33, 44, 67, 47, 66, 130, 65, 129, 517, 260, 516, 259, 515, 258, 514, 257, 513, 4101, 1025, 4100, 2049, 4099, 16388, 4098, 16387, 4097, 16386, 8193, 16385, 262150, 32769, 262149, 65537, 262148, 131073, 262147, 524291, 262146, 524290, 262145, 524289
Offset: 1

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Author

Philipp O. Tsvetkov, Jul 30 2018

Keywords

Comments

OFF cells outside the triangle of active cells are ignored.
This is also the position at which n appears for the first time in A100053.

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 .
1 OFF cell (0) appears for the first time in generation (line) 4, thus a(1) = 4;
2 consecutive OFF cells (00) appear for the first time in generation (line) 3, thus a(2) = 3;
5 consecutive OFF cells (00000) appear for the first time in generation (line) 9, thus a(5) = 9;
...
		

Crossrefs

Cf. A100053.

Programs

  • C
    See Links section.
  • Mathematica
    CellularAutomaton[30, {{1}, 0}, 10000];
    (Reverse[Internal`DeleteTrailingZeros[
          Reverse[Internal`DeleteTrailingZeros[#]]]]) & /@ %;
    Table[Position[(Max@FoldList[If[#2 == 0, #1 + 1, 0] &, 0, #]) & /@ %, i] //
       Flatten // First, {i, 1, 29}]

Extensions

a(30)-a(36) from Robert G. Wilson v, Aug 07 2018
Data corrected and more terms from Rémy Sigrist, Jul 06 2020