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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 Table of n, a(n) for n=2..87. 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. Cf. A107907, A319416, A329860, A329861, A329865, A329867. Sequence in context: A047110 A288533 A093869 * A057431 A179541 A057060 Adjacent sequences: A329867 A329868 A329869 * A329871 A329872 A329873 KEYWORD nonn AUTHOR Gus Wiseman, Nov 25 2019 STATUS approved

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