A080634 - OEIS

%I #2 Mar 30 2012 17:37:52

%S 1,2,1,2,2,1,2,1,2,1,1,2,1,2,1,2,1,2,2,1,2,2,1,1,2,1,2,1,2,2,2,1,1,1,

%T 2,2,1,2,1,1,2,2,2,1,1,1,2,1,1,2,1,2,1,2,1,2,1,1,2,2,2,2,2,1,2,1,1,1,

%U 2,1,2,2,2,1,2,2,1,2,1,2,1,2,1,1,2,1,2,2,2,1,2,1,1,2,1,2,1,1,2,2,2,1,2,1,2

%N Start with a(1)=1. Then, for n>1, choose a(n)=1 or 2 so as to minimize the longest arithmetic progression in either S1(n) or S2(n), where S1(n)={k|a(k)=1,1<=k<=n} and S2(n)={k|a(k)=2,1<=k<=n}.

%e Given the first seven terms as {1,2,1,2,2,1,2}, we find that a(8)=1 gives S1(8)={1,3,6,8}, S2(8)={2,4,5,7}, both with maximum AP's of length 2, whereas a(8)=2 gives S1(8)={1,3,6}, S2(8)={2,4,5,7,8}, with max length AP's of 2 for S1 and 3 for S2. So a(8) must be assigned the value of 1.

%K nonn

%O 1,2

%A _John W. Layman_, Feb 27 2003