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A175326 A positive integer n is included if the run-lengths (of runs both of 0's and of 1's) of the binary representation of n form an arithmetic progression (when written in order).

%I A175326 #15 Mar 11 2014 01:32:52
%S A175326 1,2,3,4,5,6,7,8,10,12,14,15,16,21,24,28,30,31,32,39,42,48,51,56,57,
%T A175326 60,62,63,64,85,96,112,120,124,126,127,128,170,192,204,224,240,248,
%U A175326 252,254,255,256,287,341,384,399,448,455,480,483,496,497,504
%N A175326 A positive integer n is included if the run-lengths (of runs both of 0's and of 1's) of the binary representation of n form an arithmetic progression (when written in order).
%C A175326 The difference between the lengths of consecutive runs in binary n may be either positive, 0, or negative.
%C A175326 This sequence provides a way to order all of the finite sequences each of positive integers arranged in an arithmetic progression (with common difference between consecutive integers being either positive, zero, or negative). See A175327.
%H A175326 Lars Blomberg, <a href="/A175326/b175326.txt">Table of n, a(n) for n = 1..10000</a>
%H A175326 Lars Blomberg, <a href="/A175326/a175326.cs.txt">C# program for generating the b-file</a>
%e A175326 57 in binary is 111001. The run lengths are therefore 3,2,1, and (3,2,1) forms an arithmetic progression; so 57 is in this sequence.
%t A175326 Select[Range@504, 2 > Length@Union@Differences[Length /@ Split@IntegerDigits[#, 2]] &] (* _Giovanni Resta_, Feb 15 2013 *)
%Y A175326 Cf. A175327, A175328.
%K A175326 base,nonn
%O A175326 1,2
%A A175326 _Leroy Quet_, Apr 07 2010
%E A175326 a(30)-a(58) from _Lars Blomberg_, Feb 15 2013