1,2

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})

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

x={100110100100110110100}

RUNS(x)={12211212212112}

RUNS^2(x)={1221121121}

RUNS^3(x)={1221211}

RUNS^4(x)={12112}

RUNS^5(x)={1121}

RUNS^6(x)={211}

RUNS^7(x)={12}

RUNS^8(x)={11}

RUNS^9(x)={2}

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.

Sequence in context: A133344 A091334 A025280 this_sequence A007600 A091333 A005245

Adjacent sequences: A096362 A096363 A096364 this_sequence A096366 A096367 A096368

nonn

John W. Layman (layman(AT)math.vt.edu), Jul 01 2004