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A329870 Runs-resistance of the binary expansion of n without the first digit. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
2,4
COMMENTS
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.
LINKS
EXAMPLE
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)
MATHEMATICA
Table[Length[NestWhileList[Length/@Split[#]&, Rest[IntegerDigits[n, 2]], Length[#]>1&]]-1, {n, 2, 100}]
CROSSREFS
Keeping the first digit gives A318928.
Cuts-resistance is A319420.
Compositions counted by runs-resistance are A329744.
Binary words counted by runs-resistance are A319411 and A329767.
Sequence in context: A047110 A288533 A093869 * A057431 A179541 A057060
KEYWORD
nonn
AUTHOR
Gus Wiseman, Nov 25 2019
STATUS
approved

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Last modified June 14 04:49 EDT 2024. Contains 373393 sequences. (Running on oeis4.)