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A248396
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"Look and say" sequence, but say everything mod 2; starting with 1101.
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2
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1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1
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OFFSET
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1
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COMMENTS
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Similar to A248392, only now the initial number is 1101 rather than 1. See A248392 for more details. A248392 and this sequence are the two most interesting fractal structures they discovered.
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REFERENCES
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Alex Kontorovich, Verbal communication to N. J. A. Sloane, Oct 16 2014, describing work that he and Sam Payne did around 1998.
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LINKS
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EXAMPLE
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The initial "numbers" are:
1101
011011
10011001
1100010011
0110110001
100110011011
11000100011001
01101110010011
1001101100110001
110001100100011011
011001001110011001
10010011001100010011
1100110001000110110001
0100011011100110011011
101110011011000100011001
11101100011001101110010011
11100110010001101100110001
11000100111001100100011011
01101100110001001110011001
1001100100011011001100010011
110001001110011001000110110001
...
The illustration gives a longer list and shows the fractal-like structure more clearly.
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MAPLE
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# a[n] is the n-th "number" read from right to left.
a[1]:=[1, 0, 1, 1]:
M:=32:
for n from 1 to M do
s:=a[n-1][1]; a[n]:=[]; r:=1;
for i from 2 to nops(a[n-1]) do
t:=a[n-1][i];
if s=t then r:=r+1;
else a[n]:=[op(a[n]), s, r mod 2]; s:=t; r:=1;
fi;
od:
a[n]:=[op(a[n]), s, r mod 2];
od:
for n from 1 to M do m:=nops(a[n]); lprint([seq(a[n][m-i+1], i=1..m)]); od:
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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