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%I #15 Mar 11 2014 01:32:52
%S 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 60,62,63,64,85,96,112,120,124,126,127,128,170,192,204,224,240,248,
%U 252,254,255,256,287,341,384,399,448,455,480,483,496,497,504
%N 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 The difference between the lengths of consecutive runs in binary n may be either positive, 0, or negative.
%C 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 Lars Blomberg, <a href="/A175326/b175326.txt">Table of n, a(n) for n = 1..10000</a>
%H Lars Blomberg, <a href="/A175326/a175326.cs.txt">C# program for generating the b-file</a>
%e 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 Select[Range@504, 2 > Length@Union@Differences[Length /@ Split@IntegerDigits[#, 2]] &] (* _Giovanni Resta_, Feb 15 2013 *)
%Y Cf. A175327, A175328.
%K base,nonn
%O 1,2
%A _Leroy Quet_, Apr 07 2010
%E a(30)-a(58) from _Lars Blomberg_, Feb 15 2013
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