cp's OEIS Frontend

A369172 Irregular triangle read by rows: row n lists the lengths of the strings of the MIU formal system at the n-th level of the tree generated by recursively applying the system rules, starting from the MI string.

%I A369172 #27 Jan 18 2024 07:47:54
%S A369172 2,3,3,5,4,5,9,7,6,9,3,3,17,13,11,4,4,10,17,7,7,7,7,7,7,4,5,5,33,25,
%T A369172 21,9,9,9,9,7,7,2,19,8,8,8,8,8,8,18,33,15,15,15,15,15,15,15,15,15,15,
%U A369172 15,15,15,15,8,13,5,5,5,8,13,5,5,8,13,5,8,13,5,8,13,5,5,13,5,5,5,7,6,9,9
%N A369172 Irregular triangle read by rows: row n lists the lengths of the strings of the MIU formal system at the n-th level of the tree generated by recursively applying the system rules, starting from the MI string.
%C A369172 See A368946 for the description of the MIU formal system and the triangle of corresponding strings.
%D A369172 Douglas R. Hofstadter, Gödel, Escher, Bach: an Eternal Golden Braid, Basic Books, 1979, pp. 33-41 and pp. 261-262.
%H A369172 Paolo Xausa, <a href="/A369172/b369172.txt">Table of n, a(n) for n = 0..3670</a> (rows 0..7 of the triangle, flattened).
%H A369172 Wikipedia, <a href="https://en.wikipedia.org/wiki/MU_puzzle">MU Puzzle</a>.
%H A369172 <a href="/index/Go#GEB">Index entries for sequences from "Goedel, Escher, Bach"</a>.
%F A369172 T(n,k) = A055642(A368946(n,k)).
%F A369172 T(n,k) = A369206(n,k) + A369207(n,k) + 1.
%e A369172 Triangle begins:
%e A369172   [0]  2;
%e A369172   [1]  3  3;
%e A369172   [2]  5  4  5;
%e A369172   [3]  9  7  6  9  3  3;
%e A369172   [4] 17 13 11  4  4 10 17  7  7  7  7  7  7  4  5  5;
%e A369172   ...
%t A369172 MIUStepOW3[s_] := Flatten[Map[{If[StringEndsQ[#, "1"], # <> "0", Nothing], # <> #, StringReplaceList[#, "111" -> "0"], StringReplaceList[#, "00" -> ""]}&, s]];
%t A369172 With[{rowmax = 5}, StringLength[NestList[MIUStepOW3, {"1"}, rowmax]]] + 1
%Y A369172 Cf. A055642, A368946, A368947 (row lengths), A369206, A369207.
%K A369172 nonn,tabf
%O A369172 0,1
%A A369172 _Paolo Xausa_, Jan 15 2024