A305260 A linear mapping a(n) = x + y*n of pairs of nonnegative integers (x,y), where the pairs are enumerated first by radial coordinate r and in case of ties, by polar angle 0 <= phi <= Pi/2 in a polar coordinate system.

0, 1, 2, 4, 2, 10, 8, 15, 18, 3, 30, 14, 37, 29, 44, 4, 64, 21, 73, 60, 44, 86, 5, 73, 99, 125, 31, 136, 61, 147, 124, 98, 163, 6, 204, 41, 217, 80, 230, 161, 204, 129, 255, 7, 308, 52, 235, 330, 198, 298, 107, 359, 163, 374, 276, 335, 8, 456, 66, 243, 424, 489, 132, 506, 390, 203, 531

Offset: 0

Author

Hugo Pfoertner, Jun 15 2018

Keywords

• nonn

Comments

Secondary sorting by polar angle is equivalent to secondary sorting by y.

The sequence is an alternative solution to the riddle described in the comments of A304584.

Examples

			   y:
     |
   8 |  57  61  63  66  70
     |
   7 |  44  47  51  53  60  68
     |
   6 |  34  36  38  42  49  55  64
     |
   5 |  25  27  29  32  40  46  54  67
     |
   4 |  16  18  21  24  30  39  48  59  69
     |
   3 |  10  12  14  19  23  31  41  52  65
     |
   2 |   5   7   8  13  20  28  37  50  62
     |
   1 |   2   3   6  11  17  26  35  45  58
     |
   0 |   0   1   4   9  15  22  33  43  56  71
       _______________________________________
  x:     0   1   2   3   4   5   6   7   8   9
.
a(5) = x(5) + 5*y(5) = 0 + 5*2 = 10,
a(14) = x(14) + 14*y(14) = 2 + 14*3 = 44,
a(20) = x(20) + 20*y(20) = 4 + 20*2 = 44.
		

Crossrefs

Cf. A000925, A283305, A283306, A304584, A304585.

Programs

PARI

n=-1;for(r2=0,81,for(y=0,round(sqrt(r2)),x2=r2-y^2;if(issquare(x2),print1(round(sqrt(x2))+y*(n++),", "))))