A164712 - OEIS

%I #15 Nov 06 2017 02:52:26

%S 10,21,22,26,36,42,43,45,46,53,54,58,73,76,85,86,87,90,91,93,94,100,

%T 106,107,109,110,117,118,122,136,147,153,156,170,171,173,174,175,181,

%U 182,183,186,187,189,190,201,204,213,214,215,218,219,221,222,228,234,235

%N 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.

%C 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.

%H Harvey P. Dale, <a href="/A164712/b164712.txt">Table of n, a(n) for n = 1..1000</a>

%e 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

%t 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 *)

%t Select[Range[2^8], And[Length@ # > 1, Length@ Union@ # == 1] &@ Map[Length, Select[Split@ IntegerDigits[#, 2], First@ # == 0 &]] &] (* _Michael De Vlieger_, Nov 04 2017 *)

%Y Cf. A164710.

%K base,nonn

%O 1,1

%A _Leroy Quet_, Aug 23 2009

%E More terms from _Sean A. Irvine_, Sep 28 2009