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A096365
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Maximum number of iterations of the RUNS transform needed to reduce any binary sequence of length n to a sequence of length 1.
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0
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0, 2, 3, 4, 5, 5, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 9
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| 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})
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EXAMPLE
| 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.
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CROSSREFS
| Sequence in context: A133344 A091334 A025280 * A200311 A007600 A195872
Adjacent sequences: A096362 A096363 A096364 * A096366 A096367 A096368
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KEYWORD
| nonn
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AUTHOR
| John W. Layman (layman(AT)math.vt.edu), Jul 01 2004
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