A164712 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

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.

LINKS

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

EXAMPLE

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

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 *)

CROSSREFS

Cf. A164710.

Sequence in context: A251128 A244539 A335236 * A336558 A374897 A338908

Adjacent sequences: A164709 A164710 A164711 * A164713 A164714 A164715

KEYWORD

base,nonn

AUTHOR

Leroy Quet, Aug 23 2009

EXTENSIONS

More terms from Sean A. Irvine, Sep 28 2009

STATUS

approved