A183993 "Types" (parities of i and j) when all the numbers i+j*r are ranked, where r=golden ratio, i>=0, j>=0.

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, 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, 3, 4, 1, 2, 4, 3, 2, 1, 4, 3, 1, 2

Offset: 1

Author

Clark Kimberling, Jan 08 2011

Keywords

• nonn

Examples

			(See the examples at A183989-A183992.)
		

Crossrefs

Cf. A001622, A183987, A183988, A183989, A183990, A183991, A183992.

Formula

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

a(n)=1 if i(n) is odd and j(n) is odd (n in A183989);

a(n)=2 if i(n) is odd and j(n) is even (n in A183990);

a(n)=3 if i(n) is even and j(n) is odd (n in A183991);

a(n)=4 if i(n) is even and j(n) is even (n in A183992).

Extensions

I edited the definition slightly. - N. J. A. Sloane, Jan 11 2011