%I A096365
%S A096365 0,2,3,4,5,5,6,6,6,7,7,7,7,8,8,8,8,8,8,8,9
%N A096365 Maximum number of iterations of the RUNS transform needed to reduce any 
               binary sequence of length n to a sequence of length 1.
%C A096365 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 A096365 The following example shows that a(21)>=9:
%e A096365 x={100110100100110110100}
%e A096365 RUNS(x)={12211212212112}
%e A096365 RUNS^2(x)={1221121121}
%e A096365 RUNS^3(x)={1221211}
%e A096365 RUNS^4(x)={12112}
%e A096365 RUNS^5(x)={1121}
%e A096365 RUNS^6(x)={211}
%e A096365 RUNS^7(x)={12}
%e A096365 RUNS^8(x)={11}
%e A096365 RUNS^9(x)={2}
%e A096365 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 A096365 Sequence in context: A133344 A091334 A025280 this_sequence A007600 A091333 
               A005245
%Y A096365 Adjacent sequences: A096362 A096363 A096364 this_sequence A096366 A096367 
               A096368
%K A096365 nonn
%O A096365 1,2
%A A096365 John W. Layman (layman(AT)math.vt.edu), Jul 01 2004