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A368947
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Row lengths of A368946: in the MIU formal system, number of (possibly not distinct) strings n steps distant from the MI string.
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6
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1, 2, 3, 6, 16, 60, 356, 3227, 44310, 928650, 28577371, 1296940642
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,2
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COMMENTS
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See A368946 for the description of the MIU formal system.
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REFERENCES
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Douglas R. Hofstadter, Gödel, Escher, Bach: an Eternal Golden Braid, Basic Books, 1979, pp. 33-41.
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LINKS
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FORMULA
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MATHEMATICA
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MIUStepW3[s_] := Flatten[Map[{If[StringEndsQ[#, "1"], # <> "0", Nothing], # <> #, StringReplaceList[#, {"111" -> "0", "00" -> ""}]}&, s]];
With[{rowmax = 9}, Map[Length, NestList[MIUStepW3, {"1"}, rowmax]]]
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PROG
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(Python)
from itertools import islice
def occurrence_swaps(w, s, t):
out, oi = [], w.find(s)
while oi != -1:
out.append(w[:oi] + t + w[oi+len(s):])
oi = w.find(s, oi+1)
return out
def moves(w): # moves for word w in MIU system, encoded as 310
nxt = []
if w[-1] == '1': nxt.append(w + '0') # Rule 1
if w[0] == '3': nxt.append(w + w[1:]) # Rule 2
nxt.extend(occurrence_swaps(w, '111', '0')) # Rule 3
nxt.extend(occurrence_swaps(w, '00', '')) # Rule 4
return nxt
def agen(): # generator of terms
frontier = ['31']
while len(frontier) > 0:
yield len(frontier)
reach1 = [m for p in frontier for m in moves(p)]
frontier, reach1 = reach1, []
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CROSSREFS
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KEYWORD
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nonn,hard,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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