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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.
1
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.
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
KEYWORD
nonn
AUTHOR
Hugo Pfoertner, Jun 15 2018
STATUS
approved