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

0,3

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.

Links

Table of n, a(n) for n=0..66.

Example

   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.

Prog

(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++), ", "))))

Crossrefs

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

Sequence in context: A097577 A097692 A118920 * A162982 A259707 A335866

Adjacent sequences: A305257 A305258 A305259 * A305261 A305262 A305263

Keyword

nonn

Author

Hugo Pfoertner, Jun 15 2018

Status

approved