cp's OEIS Frontend

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

%I A329862 #5 Nov 24 2019 09:59:53
%S A329862 3,4,6,9,11,12,13,18,19,20,22,25,26,37,38,41,43,44,45,50,51,52,53,74,
%T A329862 75,76,77,82,83,84,86,89,90,101,102,105,106,149,150,153,154,165,166,
%U A329862 169,171,172,173,178,179,180,181,202,203,204,205,210,211,212,213
%N A329862 Positive integers whose binary expansion has cuts-resistance 2.
%C A329862 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.
%H A329862 Claude Lenormand, <a href="/A318921/a318921.pdf">Deux transformations sur les mots</a>, Preprint, 5 pages, Nov 17 2003.
%e A329862 The sequence of terms together with their binary expansions begins:
%e A329862    3:      11
%e A329862    4:     100
%e A329862    6:     110
%e A329862    9:    1001
%e A329862   11:    1011
%e A329862   12:    1100
%e A329862   13:    1101
%e A329862   18:   10010
%e A329862   19:   10011
%e A329862   20:   10100
%e A329862   22:   10110
%e A329862   25:   11001
%e A329862   26:   11010
%e A329862   37:  100101
%e A329862   38:  100110
%e A329862   41:  101001
%e A329862   43:  101011
%e A329862   44:  101100
%e A329862   45:  101101
%e A329862   50:  110010
%t A329862 degdep[q_]:=Length[NestWhileList[Join@@Rest/@Split[#]&,q,Length[#]>0&]]-1;
%t A329862 Select[Range[100],degdep[IntegerDigits[#,2]]==2&]
%Y A329862 Positions of 2's in A319416.
%Y A329862 Numbers whose binary expansion has cuts-resistance 1 are A000975.
%Y A329862 Binary words with cuts-resistance 2 are conjectured to be A027383.
%Y A329862 Compositions with cuts-resistance 2 are A329863.
%Y A329862 Cuts-resistance of binary expansion without first digit is A319420.
%Y A329862 Binary words counted by cuts-resistance are A319421 and A329860.
%Y A329862 Compositions counted by cuts-resistance are A329861.
%Y A329862 Cf. A107907, A114901, A164707, A318928, A319411, A329745, A329865, A329866.
%K A329862 nonn
%O A329862 1,1
%A A329862 _Gus Wiseman_, Nov 23 2019