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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
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(163-n). [Corrected by Jinyuan Wang, Mar 08 2020]
LINKS
MIT Mistery Hunt, The Next Generation, 2018.
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
Sequence in context: A047478 A048974 A089193 * A284742 A111083 A050550
KEYWORD
nonn,fini,full
AUTHOR
Tanya Khovanova, Apr 08 2018
STATUS
approved