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"Types" (parities of i and j) when all the numbers ir+j are ranked, where r=golden ratio, i>=0, j>=0.
3

%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