Revision History for A096365
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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.
(history;
published version)
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#5 by R. J. Mathar at Mon Oct 08 09:57:20 EDT 2018
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#4 by R. J. Mathar at Mon Oct 08 09:57:15 EDT 2018
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| CROSSREFS
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Cf. A319412
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| STATUS
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approved
editing
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#3 by Russ Cox at Fri Mar 30 17:37:53 EDT 2012
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| AUTHOR
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_John W. Layman (layman(AT)math.vt.edu), _, Jul 01 2004
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Discussion
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| Fri Mar 30
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| OEIS Server: https://oeis.org/edit/global/182
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#2 by N. J. A. Sloane at Sat Nov 10 03:00:00 EST 2007
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| COMMENTS
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The RUNS transform maps a finite word (or sequence) x to the (finite) sequence y whose ithi-th term is the length of the ithi-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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| KEYWORD
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nonn,new
nonn
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#1 by N. J. A. Sloane at Wed Sep 22 03:00:00 EDT 2004
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| NAME
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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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| DATA
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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
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| OFFSET
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1,2
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| COMMENTS
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The RUNS transform maps a finite word (or sequence) x to the (finite) sequence y whose ith term is the length of the ith 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
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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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| KEYWORD
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nonn
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| AUTHOR
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John W. Layman (layman(AT)math.vt.edu), Jul 01 2004
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| STATUS
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approved
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