OFFSET
1,1
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.
LINKS
Claude Lenormand, Deux transformations sur les mots, Preprint, 5 pages, Nov 17 2003.
EXAMPLE
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
MATHEMATICA
degdep[q_]:=Length[NestWhileList[Join@@Rest/@Split[#]&, q, Length[#]>0&]]-1;
Select[Range[100], degdep[IntegerDigits[#, 2]]==2&]
CROSSREFS
Positions of 2's in A319416.
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.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Nov 23 2019
STATUS
approved