%I #12 Sep 10 2020 03:39:52
%S 1,1,3,2,3,3,4,2,3,3,3,4,5,4,4,2,3,3,3,5,3,3,4,4,5,5,4,4,5,4,4,2,3,3,
%T 3,5,3,3,5,5,3,3,3,4,7,4,4,4,5,5,5,5,7,4,4,4,5,5,4,4,5,4,4,2,3,3,3,5,
%U 3,3,5,5,3,3,3,6,5,7,5,5,3,3,3,6,3,3,4,4,7,7,4,4,8,4,4,4,5,5,5,5,5,7
%N Greatest size of an arithmetic progression contained as substrings in binary representation of n.
%C a(n) <= A078822(n);
%C a(A091461(n))=n and a(m)<>n for m < A091461(n).
%H Álvar Ibeas, <a href="/A091460/b091460.txt">Table of n, a(n) for n = 0..10000</a>
%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%e n=28->'11100', {0+k*1: 0<=k<a(28)=5}: bbbb0 => bb1bb => bb10b => b11bb => bb100;
%e n=29->'11101', {1+k*2: 0<=k<a(29)=4}: bbbb1 => b11bb => bb101 => 111bb.
%Y Cf. A078822, A007088.
%K nonn,base
%O 0,3
%A _Reinhard Zumkeller_, Jan 12 2004