A248392 "Look and say" sequence, but say everything mod 2; starting with 1.

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

Table of n, a(n) for n=1..107.

Alex Kontorovich, Programs

Alex Kontorovich, Illustration of initial terms

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

Adjacent sequences: A248389 A248390 A248391 * A248393 A248394 A248395

Keyword

nonn,base

Author

N. J. A. Sloane, Oct 17 2014

Status

approved