

A330029


Numbers whose binary expansion has cutsresistance <= 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
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OFFSET

1,3


COMMENTS

For the operation of shortening all runs by 1, cutsresistance 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 runlengths 1 or 2 and whose sequence of runlengths has no oddlength run of 1's sandwiched between two 2's.


LINKS



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

Balanced binary words are counted by A027383.
Compositions with cutsresistance <= 2 are A330028.
Cutsresistance of binary expansion is A319416.


KEYWORD

nonn


AUTHOR



STATUS

approved



