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A329870
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Runs-resistance of the binary expansion of n without the first digit.
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3
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0, 0, 1, 2, 2, 1, 1, 3, 2, 3, 3, 2, 3, 1, 1, 3, 4, 2, 4, 2, 3, 3, 3, 3, 2, 4, 2, 4, 3, 1, 1, 3, 4, 3, 3, 4, 4, 3, 4, 5, 2, 4, 4, 5, 3, 3, 3, 3, 5, 4, 4, 2, 5, 4, 3, 4, 4, 3, 3, 4, 3, 1, 1, 3, 4, 3, 3, 4, 3, 2, 3, 3, 4, 4, 2, 3, 3, 3, 4, 5, 4, 3, 4, 2, 5, 4
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internal format)
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OFFSET
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2,4
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COMMENTS
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For the operation of taking the sequence of run-lengths of a finite sequence, runs-resistance is defined to be the number of applications required to reach a singleton.
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LINKS
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EXAMPLE
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Minimal representatives with each image are:
2: (0)
4: (0,0) -> (2)
5: (0,1) -> (1,1) -> (2)
9: (0,0,1) -> (2,1) -> (1,1) -> (2)
18: (0,0,1,0) -> (2,1,1) -> (1,2) -> (1,1) -> (2)
41: (0,1,0,0,1) -> (1,1,2,1) -> (2,1,1) -> (1,2) -> (1,1) -> (2)
150: (0,0,1,0,1,1,0) -> (2,1,1,2,1) -> (1,2,1,1) -> (1,1,2) -> (2,1) -> (1,1) -> (2)
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MATHEMATICA
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Table[Length[NestWhileList[Length/@Split[#]&, Rest[IntegerDigits[n, 2]], Length[#]>1&]]-1, {n, 2, 100}]
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CROSSREFS
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Keeping the first digit gives A318928.
Compositions counted by runs-resistance are A329744.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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