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.

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

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