A330029 - OEIS

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A330029

Numbers whose binary expansion has cuts-resistance <= 2.

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:

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 * A368841 A201992 A329297

Adjacent sequences: A330026 A330027 A330028 * A330030 A330031 A330032

KEYWORD

nonn

AUTHOR

Gus Wiseman, Nov 27 2019

STATUS

approved