A164714 A positive integer n is included if all runs of 0's in binary n are of the same length, and if all runs of 1's in binary n are of the same length, and if there are at least two runs of 0's and at least two runs of 1's.

10, 21, 36, 42, 54, 73, 85, 136, 170, 204, 219, 238, 273, 292, 341, 438, 528, 585, 682, 792, 819, 924, 990, 1057, 1365, 1755, 1911, 2080, 2184, 2340, 2730, 3120, 3171, 3276, 3510, 3640, 3822, 3900, 4030, 4161, 4369, 4681, 5461, 7399, 8256, 10922, 12384

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.

The length of each run of 1's may be different that the length of each run of 0's.

This sequence contains those positive integers in both sequence A164709 and sequence A164712.

The integers of this sequence, along with those positive integers that have (when written in binary) only one run of 0's and/or only one run of 1's, make up sequence A164713.

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..100

Crossrefs

A164709, A164712, A164713

Programs

Mathematica

bslQ[n_]:=Module[{r=Split[IntegerDigits[n,2]]},Length[r]>3&&Length[ Union[ Length/@Take[r,{1,-1,2}]]]==1&&Length[Union[Length/@Take[r,{2,-1,2}]]] == 1]; Select[Range[13000],bslQ] (* Harvey P. Dale, Jan 13 2021 *)

Extensions

More terms from Sean A. Irvine, Sep 28 2009