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A166253
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String substitution 0 -> 01110, 1 -> 10001, started with 1.
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1
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1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1
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OFFSET
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1,1
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COMMENTS
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Connected to the Koch curve by doing the following repeatedly: Go one step; turn left if there is 01 or 10 in S and right if there is 00 or 11 in S. Go to the next element of the sequence.
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LINKS
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Table of n, a(n) for n=1..135.
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FORMULA
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s(0)=0,1,1,1,0 and s(1)=1,0,0,0,1 Then S = lim s^n (n to infinity)
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MATHEMATICA
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s[0] = {0, 1, 1, 1, 0}; s[1] = {1, 0, 0, 0, 1}; sf[l_] := Module[{out = {}}, For[i = 1, i <= Length[l], i++, next = l[[i]]; AppendTo[out, s[next]]]; Return[Flatten[out]]] k = 7; e = {0}; For[m = 1, m <= k, m++, e = sf[e]]; e
Nest[Flatten[#/.{0->{0, 1, 1, 1, 0}, 1->{1, 0, 0, 0, 1}}]&, 1, 6] (* Harvey P. Dale, Jul 31 2021 *)
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CROSSREFS
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Sequence in context: A267868 A288733 A095111 * A159638 A187615 A120528
Adjacent sequences: A166250 A166251 A166252 * A166254 A166255 A166256
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KEYWORD
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nonn,uned
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AUTHOR
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Stephan Rosebrock (rosebrock(AT)ph-karlsruhe.de), Oct 10 2009
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EXTENSIONS
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a(25+) corrected by Ryan Hendrickson, Apr 10 2011
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STATUS
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approved
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