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 A330029 Numbers whose binary expansion has cuts-resistance <= 2. 1
 0, 1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 13, 18, 19, 20, 21, 22, 25, 26, 37, 38, 41, 42, 43, 44, 45, 50, 51, 52, 53, 74, 75, 76, 77, 82, 83, 84, 85, 86, 89, 90, 101, 102, 105, 106, 149, 150, 153, 154, 165, 166, 169, 170, 171, 172, 173, 178, 179, 180, 181, 202, 203 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS For the operation of shortening all runs by 1, cuts-resistance is defined to be the number of applications required to reach an empty word. Also numbers whose binary expansion is a balanced word (see A027383 for definition). Also numbers whose binary expansion has all run-lengths 1 or 2 and whose sequence of run-lengths has no odd-length run of 1's sandwiched between two 2's. LINKS Table of n, a(n) for n=1..62. EXAMPLE The sequence of terms together with their binary expansions begins: 0: 1: 1 2: 10 3: 11 4: 100 5: 101 6: 110 9: 1001 10: 1010 11: 1011 12: 1100 13: 1101 18: 10010 19: 10011 20: 10100 21: 10101 22: 10110 25: 11001 26: 11010 37: 100101 38: 100110 MATHEMATICA degdep[q_]:=Length[NestWhileList[Join@@Rest/@Split[#]&, q, Length[#]>0&]]-1; Select[Range[0, 100], degdep[IntegerDigits[#, 2]]<=2&] CROSSREFS Union of A000975 and A329862. Balanced binary words are counted by A027383. Compositions with cuts-resistance <= 2 are A330028. Cuts-resistance of binary expansion is A319416. Cf. A027383, A098504, A107907, A164707, A329860, A329861, A329863, A329865. Sequence in context: A023776 A063037 A286262 * A201992 A329297 A236562 Adjacent sequences: A330026 A330027 A330028 * A330030 A330031 A330032 KEYWORD nonn AUTHOR Gus Wiseman, Nov 27 2019 STATUS approved

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Last modified September 27 20:41 EDT 2023. Contains 365714 sequences. (Running on oeis4.)