OFFSET

1,1

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.

LINKS

Rémy Sigrist, C program for A317530

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 .

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;

...

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}]

PROG

(C) See Links section.

CROSSREFS

KEYWORD

nonn

AUTHOR

Philipp O. Tsvetkov, Jul 30 2018

EXTENSIONS

a(30)-a(36) from Robert G. Wilson v, Aug 07 2018

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

STATUS

approved