A308175 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) = t(n), while the length of S is given in A308174.

2, 1, 4, 1, 5, 4, 8, 4, 7, 2, 8, 12, 2, 13, 10, 17, 7, 3, 8, 19, 14, 3, 15, 21, 19, 24, 18, 28, 17, 25, 27, 19, 34, 9, 23, 7, 38, 21, 32, 20, 38, 14, 30, 34, 29, 45, 24, 39, 35, 4, 36, 41, 27, 49, 33, 54, 36, 52, 41, 4, 42, 54, 39, 31, 65, 24, 44, 9, 36, 53

Offset

3,1

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 A308175

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, A308174.

Sequence in context: A218970 A216952 A114326 * A241423 A323244 A329642

Adjacent sequences: A308172 A308173 A308174 * A308176 A308177 A308178

Keyword

nonn,look

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