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A329862
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Positive integers whose binary expansion has cuts-resistance 2.
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9
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3, 4, 6, 9, 11, 12, 13, 18, 19, 20, 22, 25, 26, 37, 38, 41, 43, 44, 45, 50, 51, 52, 53, 74, 75, 76, 77, 82, 83, 84, 86, 89, 90, 101, 102, 105, 106, 149, 150, 153, 154, 165, 166, 169, 171, 172, 173, 178, 179, 180, 181, 202, 203, 204, 205, 210, 211, 212, 213
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listen;
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internal format)
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OFFSET
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1,1
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COMMENTS
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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.
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LINKS
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EXAMPLE
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The sequence of terms together with their binary expansions begins:
3: 11
4: 100
6: 110
9: 1001
11: 1011
12: 1100
13: 1101
18: 10010
19: 10011
20: 10100
22: 10110
25: 11001
26: 11010
37: 100101
38: 100110
41: 101001
43: 101011
44: 101100
45: 101101
50: 110010
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MATHEMATICA
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degdep[q_]:=Length[NestWhileList[Join@@Rest/@Split[#]&, q, Length[#]>0&]]-1;
Select[Range[100], degdep[IntegerDigits[#, 2]]==2&]
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CROSSREFS
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Numbers whose binary expansion has cuts-resistance 1 are A000975.
Binary words with cuts-resistance 2 are conjectured to be A027383.
Compositions with cuts-resistance 2 are A329863.
Cuts-resistance of binary expansion without first digit is A319420.
Compositions counted by cuts-resistance are A329861.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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