A329862 Positive integers whose binary expansion has cuts-resistance 2.

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

Offset: 1

Author

Gus Wiseman, Nov 23 2019

Keywords

• nonn

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.

Examples

			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
		

Links

• Claude Lenormand, Deux transformations sur les mots, Preprint, 5 pages, Nov 17 2003.

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.

Binary words counted by cuts-resistance are A319421 and A329860.

Compositions counted by cuts-resistance are A329861.

Cf. A107907, A114901, A164707, A318928, A319411, A329745, A329865, A329866.

Programs

Mathematica

degdep[q_]:=Length[NestWhileList[Join@@Rest/@Split[#]&,q,Length[#]>0&]]-1;
Select[Range[100],degdep[IntegerDigits[#,2]]==2&]