A175416 - OEIS

%I #12 Mar 11 2014 01:32:53

%S 1,2,4,5,6,8,10,14,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,32,42,

%T 62,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,

%U 86,87,88,89,90,91,92,93,94,95,96,97,98,99,100

%N Those positive integers n that when written in binary, each run of 0's and 1's has a length which is coprime to the number of binary digits of n.

%H Harvey P. Dale, <a href="/A175416/b175416.txt">Table of n, a(n) for n = 1..5000</a>

%e 70 in binary is 1000110. There is a run of one 1, followed by a run of three 0's, followed by a run of two 1's, followed finally by a run of one 0. And there are seven binary digits all together. Since 1, 3, 2, and 1 each are coprime to 7, then 70 is in the sequence.

%t cpQ[n_]:=Module[{d=Length/@Split[IntegerDigits[n,2]]},And@@CoprimeQ[ d, Total[ d]]]; Select[Range[100],cpQ] (* _Harvey P. Dale_, Mar 25 2013 *)

%Y Cf. A175415

%K base,nonn

%O 1,2

%A _Leroy Quet_, May 07 2010

%E More terms from _Sean A. Irvine_, Mar 02 2011