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

Author

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

Keywords

• nonn

Comments

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

Examples

			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)
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 3..50000
• Rémy Sigrist, Perl program for A308174

Crossrefs

Cf. A038219, A308175.

Programs

Perl

See Links section.

Extensions

More terms from Rémy Sigrist, May 21 2019