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%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
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