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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 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A097577 A097692 A118920 * A162982 A259707 A335866
KEYWORD
nonn
AUTHOR
Hugo Pfoertner, Jun 15 2018
STATUS
approved

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Last modified March 29 10:59 EDT 2024. Contains 371277 sequences. (Running on oeis4.)