A308174 - OEIS

%I #17 May 22 2019 13:16:58

%S 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,

%T 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,

%U 6,6,6,5,6,6,6,6,5,5,6,6,6,6,6,6,6,6,6

%N 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.

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

%H Rémy Sigrist, <a href="/A308174/b308174.txt">Table of n, a(n) for n = 3..50000</a>

%H Rémy Sigrist, <a href="/A308174/a308174.pl.txt">Perl program for A308174</a>

%e Tableau showing calculation of terms 3 through 13

%e 1   2   3   4   5   6   7   8   9  10  11  12  13  n

%e 0   1   0   0   1   1   0   1   0   1   1   1   0  A038219(n)

%e -   -   0   0  01   1  10  01 010 101 011  11 110  S

%e -   -   1   1   2   1   2   2   3   3   3   2   3  s = A308174(n)

%e -   -   1   3   1   5   2   4   1   6   4  10   5  previous

%e -   -   2   1   4   1   5   4   8   4   7   2   8  t = A308175(n)

%e "Previous" = index of start of most recent previous occurrence of S; s = |S|; t = n - "previous" = A308175(n)

%o (Perl) See Links section.

%Y Cf. A038219, A308175.

%K nonn

%O 3,3

%A _N. J. A. Sloane_, May 21 2019, corrected and extended May 21 2019

%E More terms from _Rémy Sigrist_, May 21 2019