%N "Types" (parities of i and j) when all the numbers i+j*r are ranked, where r=sqrt(2), 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 i+j*r, where
%F r=2^(1/2) and i>=0, j>=0. Then
%F a(n)=1 if i(n) is odd and j(n) is odd (n in A184399);
%F a(n)=2 if i(n) is odd and j(n) is even (n in A184400);
%F a(n)=3 if i(n) is even and j(n) is odd (n in A184401);
%F a(n)=4 if i(n) is even and j(n) is even (n in A184402).
%e (See the examples at A184399-A184402.)
%Y Cf. A183993, A184338, A184397, A184398, A184399, A184400, A184401, A184402.
%A _Clark Kimberling_, Jan 12 2011