%I #8 Mar 30 2012 18:57:13
%S 4,3,2,4,1,3,4,2,4,3,1,2,3,4,2,1,4,3,4,1,2,3,4,3,2,1,4,2,3,4,1,2,3,1,
%T 4,3,2,4,1,4,2,3,4,1,3,2,3,1,4,2,3,2,4,1,4,2,3,1,4,1,3,2,4,3,1,4,2,3,
%U 2,4,1,3,4,2,3,1,4,2,1,3,2,4,3,1,4,2,3,1,2,4,1,3,4,2,4,3
%N "Types" (parities of i and j) when all the numbers ir+j are ranked, where r=golden ratio, i>=0, j>=0.
%F Let s(n)=i(n)*r+j(n) be the sequence obtained by arranging in increasing order all the numbers ir+j, where r is the golden mean ((1+sqrt(5))/2), and i>=0, j>=0. Then
%F a(n)=1 if i(n) is odd and j(n) is odd (n in A183989);
%F a(n)=2 if i(n) is odd and j(n) is even (n in A183991);
%F a(n)=3 if i(n) is even and j(n) is odd (n in A183990);
%F a(n)=4 if i(n) is even and j(n) is even (n in A183992).
%e (See the examples at A183989-A183991.)
%Y Cf. A184332, A184333, A183992, A183993.
%K nonn
%O 1,1
%A _Clark Kimberling_, Jan 11 2011