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"Types" (parities of i and j) when all the numbers i+j/r are ranked, where r=sqrt(2), i>=0, j>=0.
2

%I #8 Oct 16 2024 06:02:31

%S 4,3,2,4,1,4,3,2,3,4,2,1,4,3,1,2,4,3,4,2,1,3,4,3,2,1,2,4,3,4,1,2,1,4,

%T 3,4,3,2,1,2,3,4,3,2,4,1,2,1,4,3,4,1,3,2,1,4,2,3,4,3,2,4,1,2,3,1,4,3,

%U 2,4,1,3,2,1,4,2,3,4,1,3,2,4,1,4,2,3,2,4,3,2,4,1,3,2,3,1

%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)+j(n)/r be the sequence obtained by arranging in increasing order all the numbers i+j/r, where

%F r=sqrt(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 A184401);

%F a(n)=3 if i(n) is even and j(n) is odd (n in A184400);

%F a(n)=r if i(n) is even and j(n) is even (n in A184402).

%e See the examples at A184399-A184402 and A184410-A184411.

%Y Cf. A184399-A184403, A184410, A184411, A183993.

%K nonn

%O 1,1

%A _Clark Kimberling_, Jan 13 2011