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A305260
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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.
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1
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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
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OFFSET
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0,3
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COMMENTS
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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.
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LINKS
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EXAMPLE
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y:
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8 | 57 61 63 66 70
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7 | 44 47 51 53 60 68
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6 | 34 36 38 42 49 55 64
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5 | 25 27 29 32 40 46 54 67
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4 | 16 18 21 24 30 39 48 59 69
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3 | 10 12 14 19 23 31 41 52 65
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2 | 5 7 8 13 20 28 37 50 62
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1 | 2 3 6 11 17 26 35 45 58
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0 | 0 1 4 9 15 22 33 43 56 71
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x: 0 1 2 3 4 5 6 7 8 9
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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.
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PROG
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(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++), ", "))))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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