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%I #21 Mar 09 2020 05:41:31
%S 5,7,9,13,15,21,22,23,25,26,27,29,30,31,33,35,37,38,39,41,43,44,45,49,
%T 51,52,53,54,57,58,59,60,61,62,65,67,69,71,73,74,75,77,78,79,82,83,85,
%U 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
%N Elementary automaton rules that include every possible substring of length 3 in an output.
%C This sequence was important in designing the 2018 MIT Mystery Hunt puzzle "The Next Generation".
%C These are the rules that do not lose information entropy.
%C There is a symmetry: a(n) = 255 - a(163-n). [Corrected by _Jinyuan Wang_, Mar 08 2020]
%H Jinyuan Wang, <a href="/A302482/b302482.txt">Table of n, a(n) for n = 1..162</a>
%H MIT Mistery Hunt, <a href="http://web.mit.edu/puzzle/www/2018/full/puzzle/the_next_generation.html">The Next Generation</a>, 2018.
%e 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.
%t Select[Range[0, 255],
%t Length[Union[
%t Table[Take[
%t CellularAutomaton[#, IntegerDigits[n, 2, 5]], {2, 4}], {n, 0,
%t 31}]]] == 8 &]
%K nonn,fini,full
%O 1,1
%A _Tanya Khovanova_, Apr 08 2018
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