cp's OEIS Frontend

A107907 Numbers having consecutive zeros or consecutive ones in binary representation.

%I A107907 #25 Jul 30 2025 09:46:10
%S A107907 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 A107907 31,32,33,34,35,36,37,38,39,40,41,43,44,45,46,47,48,49,50,51,52,53,54,
%U A107907 55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77
%N A107907 Numbers having consecutive zeros or consecutive ones in binary representation.
%C A107907 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
%H A107907 Amiram Eldar, <a href="/A107907/b107907.txt">Table of n, a(n) for n = 1..10000</a>
%F A107907 a(A000247(n)) = A000225(n+2).
%F A107907 a(A000295(n+2)) = A000079(n+2).
%F A107907 a(A000325(n+2)) = A000051(n+2) for n>0.
%F A107907 a(n) = m+1 if m >= floor(2^k/3) otherwise a(n) = m where k = floor(log_2(3*(n+1))) and m = n-2+k. - _Chai Wah Wu_, Apr 21 2025
%e A107907 From _Gus Wiseman_, Nov 27 2019: (Start)
%e A107907 The sequence of terms together with their binary expansions begins:
%e A107907     3:      11
%e A107907     4:     100
%e A107907     6:     110
%e A107907     7:     111
%e A107907     8:    1000
%e A107907     9:    1001
%e A107907    11:    1011
%e A107907    12:    1100
%e A107907    13:    1101
%e A107907    14:    1110
%e A107907    15:    1111
%e A107907    16:   10000
%e A107907    17:   10001
%e A107907    18:   10010
%e A107907 (End)
%t A107907 Select[Range[100],MatchQ[IntegerDigits[#,2],{___,x_,x_,___}]&] (* _Gus Wiseman_, Nov 27 2019 *)
%t A107907 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 *)
%o A107907 (Python)
%o A107907 def A107907(n): return (m:=n-2+(k:=(3*n+3).bit_length()))+(m>=(1<<k)//3) # _Chai Wah Wu_, Apr 21 2025
%Y A107907 Union of A003754 and A003714.
%Y A107907 Complement of A000975.
%Y A107907 Cf. A000120, A007088, A070939, A107909, A329862.
%K A107907 nonn,base
%O A107907 1,1
%A A107907 _Reinhard Zumkeller_, May 28 2005
%E A107907 Offset changed to 1 by _Chai Wah Wu_, Apr 21 2025