cp's OEIS Frontend

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.

%I A305260 #11 Jun 18 2018 09:30:01
%S A305260 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,
%T A305260 125,31,136,61,147,124,98,163,6,204,41,217,80,230,161,204,129,255,7,
%U A305260 308,52,235,330,198,298,107,359,163,374,276,335,8,456,66,243,424,489,132,506,390,203,531
%N 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.
%C A305260 Secondary sorting by polar angle is equivalent to secondary sorting by y.
%C A305260 The sequence is an alternative solution to the riddle described in the comments of A304584.
%e A305260    y:
%e A305260      |
%e A305260    8 |  57  61  63  66  70
%e A305260      |
%e A305260    7 |  44  47  51  53  60  68
%e A305260      |
%e A305260    6 |  34  36  38  42  49  55  64
%e A305260      |
%e A305260    5 |  25  27  29  32  40  46  54  67
%e A305260      |
%e A305260    4 |  16  18  21  24  30  39  48  59  69
%e A305260      |
%e A305260    3 |  10  12  14  19  23  31  41  52  65
%e A305260      |
%e A305260    2 |   5   7   8  13  20  28  37  50  62
%e A305260      |
%e A305260    1 |   2   3   6  11  17  26  35  45  58
%e A305260      |
%e A305260    0 |   0   1   4   9  15  22  33  43  56  71
%e A305260        _______________________________________
%e A305260   x:     0   1   2   3   4   5   6   7   8   9
%e A305260 .
%e A305260 a(5) = x(5) + 5*y(5) = 0 + 5*2 = 10,
%e A305260 a(14) = x(14) + 14*y(14) = 2 + 14*3 = 44,
%e A305260 a(20) = x(20) + 20*y(20) = 4 + 20*2 = 44.
%o A305260 (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++),", "))))
%Y A305260 Cf. A000925, A283305, A283306, A304584, A304585.
%K A305260 nonn
%O A305260 0,3
%A A305260 _Hugo Pfoertner_, Jun 15 2018