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A248392
"Look and say" sequence, but say everything mod 2; starting with 1.
3
1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 1
OFFSET
1
COMMENTS
In the "Look and Say" sequence A005150 you read the previous term from left to right. For each run of consecutive equal digits, you say the length of the run followed by the digit itself.
After 6666777 for example you would say 4 6's, 3 7's, and the next term would be 4637. But now we say both the length of the run and the digit itself mod 2, so 6666777 would be read as 0 0's, 1 1, and the next term would be 0011.
We start with 1, so the initial terms are 1, 11, 01, 1011, 111001, etc. (see the Example lines).
Since this process leads to "numbers" with leading zeros, we give the sequence of successive digits instead of the successive "numbers" (so 1; 1,1; 0,1; 1,0,1,1; ...).
REFERENCES
Alex Kontorovich, Verbal communication to N. J. A. Sloane, Oct 16 2014, describing work that he and Sam Payne did around 1998.
LINKS
EXAMPLE
The initial "numbers" are:
1
11
01
1011
111001
110011
010001
10111011
1110111001
1110110011
1110010001
1100111011
0100111001
101100110011
11100100010001
11001110111011
01001110111001
1011001110110011
111001001110010001
110011001100111011
010001000100111001
10111011101100110011
1110111011100100010001
1110111011001110111011
1110111001001110111001
1110110011001110110011
1110010001001110010001
1100111011001100111011
0100111001000100111001
101100110011101100110011
11100100010011100100010001
11001110110011001110111011
...
The illustration gives a longer list and shows the fractal-like structure more clearly.
MAPLE
# a[n] is the n-th "number" read from right to left.
a[1]:=[1]: a[2]:=[1, 1]: a[3]:=[1, 0]: a[4]:=[1, 1, 0, 1]:
M:=32:
for n from 5 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:
CROSSREFS
Cf. A005150, A248393 (number of 1's in n-th "number"), A248396.
Sequence in context: A285960 A174600 A265186 * A188318 A361897 A189206
KEYWORD
nonn,base
AUTHOR
N. J. A. Sloane, Oct 17 2014
STATUS
approved