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

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, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77

Offset

0,1

Comments

Union of A003754 and A003714, complement of A000975;

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

Links

Table of n, a(n) for n=0..70.

Formula

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

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

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

Example

From Gus Wiseman, Nov 27 2019: (Start)
The sequence of terms together with their binary expansions begins:
    3:      11
    4:     100
    6:     110
    7:     111
    8:    1000
    9:    1001
   11:    1011
   12:    1100
   13:    1101
   14:    1110
   15:    1111
   16:   10000
   17:   10001
   18:   10010
(End)

Mathematica

Select[Range[100], MatchQ[IntegerDigits[#, 2], {___, x_, x_, ___}]&] (* Gus Wiseman, Nov 27 2019 *)
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 *)

Crossrefs

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

Sequence in context: A122409 A039093 A085925 * A080804 A164386 A111909

Adjacent sequences: A107904 A107905 A107906 * A107908 A107909 A107910

Keyword

nonn

Author

Reinhard Zumkeller, May 28 2005

Status

approved