

A183993


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


9



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
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OFFSET

1,1


REFERENCES

Mohammad K. Azarian, Problem 123, Missouri Journal of Mathematical Sciences, Vol. 10, No. 3, Fall 1998, p. 176. Solution published in Vol. 12, No. 1, Winter 2000, pp. 6162.


LINKS

Table of n, a(n) for n=1..80.


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).


EXAMPLE

(See the examples at A183989A183992.)


CROSSREFS

Cf. A183987, A183988, A183989, A183990, A183991, A183992.
Sequence in context: A226087 A118945 A016692 * A184403 A198120 A001390
Adjacent sequences: A183990 A183991 A183992 * A183994 A183995 A183996


KEYWORD

nonn


AUTHOR

Clark Kimberling, Jan 08 2011


EXTENSIONS

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


STATUS

approved



