A164712 A positive integer n is included if all runs of 0's in binary n are of the same length, and if there are at least two runs of 0's.

10, 21, 22, 26, 36, 42, 43, 45, 46, 53, 54, 58, 73, 76, 85, 86, 87, 90, 91, 93, 94, 100, 106, 107, 109, 110, 117, 118, 122, 136, 147, 153, 156, 170, 171, 173, 174, 175, 181, 182, 183, 186, 187, 189, 190, 201, 204, 213, 214, 215, 218, 219, 221, 222, 228, 234, 235

Offset: 1

Author

Leroy Quet, Aug 23 2009

Keywords

• base
• nonn

Comments

Clarification: A binary number consists of "runs" completely of 1's alternating with runs completely of 0's. No two or more runs all of the same digit are adjacent.

Examples

			100 is a term since its binary expansion "1100100" has two groups of zeros that are of the same length. - _Michael De Vlieger_, Nov 04 2017
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A164710.

Programs

Mathematica

brQ[n_]:=Module[{rz=Select[Split[IntegerDigits[n,2]],MemberQ[#,0]&]}, Length[ rz]>1 && Length[Union[Length/@rz]]==1]; Select[Range[250],brQ] (* Harvey P. Dale, Mar 23 2015 *)
Select[Range[2^8], And[Length@ # > 1, Length@ Union@ # == 1] &@ Map[Length, Select[Split@ IntegerDigits[#, 2], First@ # == 0 &]] &] (* Michael De Vlieger, Nov 04 2017 *)

Extensions

More terms from Sean A. Irvine, Sep 28 2009