cp's OEIS Frontend

A330029 Numbers whose binary expansion has cuts-resistance <= 2.

%I A330029 #10 Nov 29 2019 18:26:07
%S A330029 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,
%T A330029 45,50,51,52,53,74,75,76,77,82,83,84,85,86,89,90,101,102,105,106,149,
%U A330029 150,153,154,165,166,169,170,171,172,173,178,179,180,181,202,203
%N A330029 Numbers whose binary expansion has cuts-resistance <= 2.
%C A330029 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.
%C A330029 Also numbers whose binary expansion is a balanced word (see A027383 for definition).
%C A330029 Also numbers whose binary expansion has all run-lengths 1 or 2 and whose sequence of run-lengths has no odd-length run of 1's sandwiched between two 2's.
%e A330029 The sequence of terms together with their binary expansions begins:
%e A330029     0:
%e A330029     1:        1
%e A330029     2:       10
%e A330029     3:       11
%e A330029     4:      100
%e A330029     5:      101
%e A330029     6:      110
%e A330029     9:     1001
%e A330029    10:     1010
%e A330029    11:     1011
%e A330029    12:     1100
%e A330029    13:     1101
%e A330029    18:    10010
%e A330029    19:    10011
%e A330029    20:    10100
%e A330029    21:    10101
%e A330029    22:    10110
%e A330029    25:    11001
%e A330029    26:    11010
%e A330029    37:   100101
%e A330029    38:   100110
%t A330029 degdep[q_]:=Length[NestWhileList[Join@@Rest/@Split[#]&,q,Length[#]>0&]]-1;
%t A330029 Select[Range[0,100],degdep[IntegerDigits[#,2]]<=2&]
%Y A330029 Union of A000975 and A329862.
%Y A330029 Balanced binary words are counted by A027383.
%Y A330029 Compositions with cuts-resistance <= 2 are A330028.
%Y A330029 Cuts-resistance of binary expansion is A319416.
%Y A330029 Cf. A027383, A098504, A107907, A164707, A329860, A329861, A329863, A329865.
%K A330029 nonn
%O A330029 1,3
%A A330029 _Gus Wiseman_, Nov 27 2019