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%I #13 Feb 22 2023 05:36:29
%S 4,2,3,4,1,2,4,3,4,2,1,3,2,4,3,1,4,2,4,1,3,2,4,2,3,1,4,3,2,4,1,3,2,1,
%T 4,2,3,4,1,4,3,2,4,1,2,3,2,1,4,3,2,3,4,1,4,3,2,1,4,1,2,3,4,2,1,4,3,2,
%U 3,4,1,2,4,3,2,1,4,3,1,2
%N "Types" (parities of i and j) when all the numbers i+j*r 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 i+j*r, 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 A183990);
%F a(n)=3 if i(n) is even and j(n) is odd (n in A183991);
%F a(n)=4 if i(n) is even and j(n) is even (n in A183992).
%e (See the examples at A183989-A183992.)
%Y Cf. A001622, A183987, A183988, A183989, A183990, A183991, A183992.
%K nonn
%O 1,1
%A _Clark Kimberling_, Jan 08 2011
%E I edited the definition slightly. - _N. J. A. Sloane_, Jan 11 2011
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