

A280317


Ordinate of points (x,y) of the square lattice such that x >= 0 and 0 <= y <= x, and ranked in order of increasing distance from the origin. Equidistant points are ranked in order of increasing ordinate.


4



0, 0, 1, 0, 1, 2, 0, 1, 2, 0, 1, 3, 2, 0, 3, 1, 2, 4, 3, 0, 1, 2, 4, 3, 0, 1, 5, 4, 2, 3, 5, 0, 1, 4, 2, 6, 3, 5, 4, 0, 1, 2, 6, 5, 3, 4, 7, 0, 6, 1, 2, 5, 3, 7, 4, 6, 0, 1, 2, 5, 8, 3, 7, 6, 4, 0, 1, 8, 5, 2, 7, 3, 6, 4, 9, 8, 0, 5, 1, 7, 2, 3, 6, 9, 4, 8, 7, 5, 0, 1, 2, 10, 9, 3, 6, 8, 4, 7, 5, 10
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OFFSET

1,6


LINKS

Table of n, a(n) for n=1..100.


EXAMPLE

a(12) = 3 since the twelfth point in distance from the origin is (3,3) at a distance of 3*sqrt(2) = 4.242640... whereas the eleventh is (4,1) at a distance of sqrt(17) = 4.12310... and the thirteenth is (4,2) at a distance of 2*sqrt(5) = 4.472113... .
The fourteenth and fifteenth points are respectively (5,0) and (4,3) and have the same distance 5 to the origin, but (5,0) has a smaller ordinate than (4,3), so a(14) = 0 and a(15) = 3.


MATHEMATICA

xmax = 20; (* Maximum explorative abscissa *)
(* t are points in the triangle of vertices (0, 0), (0, max) and (xmax, xmax) *)
t = Flatten[Table[{x, y}, {x, 0, xmax}, {y, 0, x}], 1];
nmax = Floor[xmax^2/4] (* Safe limit for correctly sorted sequence *)
Transpose[SortBy[t, {#[[1]]^2 + #[[2]]^2 &, #[[2]] &}]][[2]][[1 ;;
nmax]]


CROSSREFS

Cf. A280079.
Sequence in context: A141100 A270655 A229140 * A283304 A058685 A351637
Adjacent sequences: A280314 A280315 A280316 * A280318 A280319 A280320


KEYWORD

nonn


AUTHOR

Robert G. Wilson v and Andres Cicuttin, Dec 31 2016


STATUS

approved



