

A302482


Elementary automaton rules that include every possible substring of length 3 in an output.


1



5, 7, 9, 13, 15, 21, 22, 23, 25, 26, 27, 29, 30, 31, 33, 35, 37, 38, 39, 41, 43, 44, 45, 49, 51, 52, 53, 54, 57, 58, 59, 60, 61, 62, 65, 67, 69, 71, 73, 74, 75, 77, 78, 79, 82, 83, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 97, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 113, 114, 115, 118, 120, 121, 122, 123, 124, 125
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

This sequence was important in designing the 2018 MIT Mystery Hunt puzzle "The Next Generation".
These are the rules that do not lose information entropy.
There is a symmetry: a(n) = 255  a(163n). [Corrected by Jinyuan Wang, Mar 08 2020]


LINKS



EXAMPLE

Consider rule 1 that outputs a one if and only if there are three zeros above it. The rule cannot have 101 as a substring in the output.


MATHEMATICA

Select[Range[0, 255],
Length[Union[
Table[Take[
CellularAutomaton[#, IntegerDigits[n, 2, 5]], {2, 4}], {n, 0,
31}]]] == 8 &]


CROSSREFS



KEYWORD

nonn,fini,full


AUTHOR



STATUS

approved



