

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
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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

Jinyuan Wang, Table of n, a(n) for n = 1..162
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
Adjacent sequences: A302479 A302480 A302481 * A302483 A302484 A302485


KEYWORD

nonn,fini,full


AUTHOR

Tanya Khovanova, Apr 08 2018


STATUS

approved



