%I #5 Oct 08 2018 09:57:20

%S 0,2,3,4,5,5,6,6,6,7,7,7,7,8,8,8,8,8,8,8,9

%N Maximum number of iterations of the RUNS transform needed to reduce any binary sequence of length n to a sequence of length 1.

%C The RUNS transform maps a finite word (or sequence) x to the (finite) sequence y whose i-th term is the length of the i-th subsequence of consecutive identical terms of x. (Example: RUNS{1,2,2,2,1,1,3,3,1}={1,3,2,2,1})

%e The following example shows that a(21)>=9:

%e x={100110100100110110100}

%e RUNS(x)={12211212212112}

%e RUNS^2(x)={1221121121}

%e RUNS^3(x)={1221211}

%e RUNS^4(x)={12112}

%e RUNS^5(x)={1121}

%e RUNS^6(x)={211}

%e RUNS^7(x)={12}

%e RUNS^8(x)={11}

%e RUNS^9(x)={2}

%e Since calculation shows that no other binary sequence of length 21 requires more than 9 iterations of RUNS to reduce it to a single term, we have a(21)=9.

%Y Cf. A319412

%K nonn

%O 1,2

%A _John W. Layman_, Jul 01 2004