A107907 - OEIS

%I #14 Jul 31 2021 15:18:30

%S 3,4,6,7,8,9,11,12,13,14,15,16,17,18,19,20,22,23,24,25,26,27,28,29,30,

%T 31,32,33,34,35,36,37,38,39,40,41,43,44,45,46,47,48,49,50,51,52,53,54,

%U 55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77

%N Numbers having consecutive zeros or consecutive ones in binary representation.

%C Union of A003754 and A003714, complement of A000975;

%C Also positive integers whose binary expansion has cuts-resistance > 1. For the operation of shortening all runs by 1, cuts-resistance is the number of applications required to reach an empty word. - _Gus Wiseman_, Nov 27 2019

%F a(A000247(n)) = A000225(n+2);

%F a(A000295(n+2)) = A000079(n+2);

%F a(A000325(n+2)) = A000051(n+2) for n>0.

%e From _Gus Wiseman_, Nov 27 2019: (Start)

%e The sequence of terms together with their binary expansions begins:

%e     3:      11

%e     4:     100

%e     6:     110

%e     7:     111

%e     8:    1000

%e     9:    1001

%e    11:    1011

%e    12:    1100

%e    13:    1101

%e    14:    1110

%e    15:    1111

%e    16:   10000

%e    17:   10001

%e    18:   10010

%e (End)

%t Select[Range[100],MatchQ[IntegerDigits[#,2],{___,x_,x_,___}]&] (* _Gus Wiseman_, Nov 27 2019 *)

%t Select[Range[80],SequenceCount[IntegerDigits[#,2],{x_,x_}]>0&] (* or *) Complement[Range[85],Table[FromDigits[PadRight[{},n,{1,0}],2],{n,7}]] (* _Harvey P. Dale_, Jul 31 2021 *)

%Y Cf. A000120, A000975, A007088, A070939, A107909, A329862.

%K nonn

%O 0,1

%A _Reinhard Zumkeller_, May 28 2005