A308174 Let EM denote the Ehrenfeucht-Mycielski sequence A038219, and let P(n) = [EM(1),...,EM(n)]. To compute EM(n+1) for n>=3, we find the longest suffix S (say) of P(n) which has previously appeared in P(n). Suppose the most recent appearance of S began at index n-t(n). Then a(n) = length of S, while t(n) is given in A308175.

1, 1, 2, 1, 2, 2, 3, 3, 3, 2, 3, 3, 2, 3, 3, 4, 4, 3, 4, 4, 4, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 6, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 5, 6, 6, 6, 6, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6

Offset

3,3

Comments

Then EM(n+1) is the complement of the bit following the most recent appearance of S.

Links

Rémy Sigrist, Table of n, a(n) for n = 3..50000

Rémy Sigrist, Perl program for A308174

Example

Tableau showing calculation of terms 3 through 13
1   2   3   4   5   6   7   8   9  10  11  12  13  n
0   1   0   0   1   1   0   1   0   1   1   1   0  A038219(n)
-   -   0   0  01   1  10  01 010 101 011  11 110  S
-   -   1   1   2   1   2   2   3   3   3   2   3  s = A308174(n)
-   -   1   3   1   5   2   4   1   6   4  10   5  previous
-   -   2   1   4   1   5   4   8   4   7   2   8  t = A308175(n)
"Previous" = index of start of most recent previous occurrence of S; s = |S|; t = n - "previous" = A308175(n)

Prog

(Perl) See Links section.

Crossrefs

Cf. A038219, A308175.

Sequence in context: A230149 A050373 A306433 * A126237 A243164 A333708

Adjacent sequences: A308171 A308172 A308173 * A308175 A308176 A308177

Keyword

nonn

Author

N. J. A. Sloane, May 21 2019, corrected and extended May 21 2019

Extensions

More terms from Rémy Sigrist, May 21 2019

Status

approved