A166253 String substitution 0 -> 01110, 1 -> 10001, started with 1.

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

Offset

1,1

Comments

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.

Links

Table of n, a(n) for n=1..135.

Formula

s(0)=0,1,1,1,0 and s(1)=1,0,0,0,1 Then S = lim s^n (n to infinity)

Mathematica

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 *)

Crossrefs

Sequence in context: A267868 A288733 A095111 * A159638 A187615 A369653

Adjacent sequences: A166250 A166251 A166252 * A166254 A166255 A166256

Keyword

nonn,uned

Author

Stephan Rosebrock (rosebrock(AT)ph-karlsruhe.de), Oct 10 2009

Extensions

a(25+) corrected by Ryan Hendrickson, Apr 10 2011

Status

approved