A302482 Elementary automaton rules that include every possible substring of length 3 in an output.

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

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