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