A160531 Those positive integers n that contain both odd-lengthed and even-lengthed runs of 0's and 1's when n is represented in binary.

4, 6, 9, 11, 13, 16, 18, 19, 20, 22, 24, 25, 26, 27, 28, 30, 33, 35, 36, 37, 38, 39, 41, 43, 44, 45, 47, 49, 50, 52, 53, 54, 55, 57, 59, 61, 64, 66, 67, 68, 70, 72, 73, 74, 75, 76, 77, 78, 79, 80, 82, 83, 84, 86, 88, 89, 90, 91, 92, 94, 96, 97, 98, 99, 100, 101, 102, 103, 104

Offset: 1

Author

Leroy Quet, May 17 2009

Keywords

• base
• nonn

Comments

Let the binary representation of n be thought of as a string of 0's and 1's. By a "run" of 0's or 1's, it is meant either a contiguous substring all of 0's bounded by 1's or the by the edge of the string, or a contiguous substring all of 1's bounded by 0's or the by the edge of the string.

This sequence contains precisely those positive integers that are in neither sequence A001196 nor sequence A160530.

Crossrefs

A001196, A160530

Programs

Mathematica

Select[Range[120],Select[l=Length/@Split[IntegerDigits[ #,2]],EvenQ]!={}&&Select[l,OddQ]!={}&] (* Ray Chandler, May 19 2009 *)

Extensions

Extended by Ray Chandler, May 19 2009