A305260 - OEIS

%I #11 Jun 18 2018 09:30:01

%S 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 125,31,136,61,147,124,98,163,6,204,41,217,80,230,161,204,129,255,7,

%U 308,52,235,330,198,298,107,359,163,374,276,335,8,456,66,243,424,489,132,506,390,203,531

%N 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 Secondary sorting by polar angle is equivalent to secondary sorting by y.

%C The sequence is an alternative solution to the riddle described in the comments of A304584.

%e    y:

%e      |

%e    8 |  57  61  63  66  70

%e      |

%e    7 |  44  47  51  53  60  68

%e      |

%e    6 |  34  36  38  42  49  55  64

%e      |

%e    5 |  25  27  29  32  40  46  54  67

%e      |

%e    4 |  16  18  21  24  30  39  48  59  69

%e      |

%e    3 |  10  12  14  19  23  31  41  52  65

%e      |

%e    2 |   5   7   8  13  20  28  37  50  62

%e      |

%e    1 |   2   3   6  11  17  26  35  45  58

%e      |

%e    0 |   0   1   4   9  15  22  33  43  56  71

%e        _______________________________________

%e   x:     0   1   2   3   4   5   6   7   8   9

%e .

%e a(5) = x(5) + 5*y(5) = 0 + 5*2 = 10,

%e a(14) = x(14) + 14*y(14) = 2 + 14*3 = 44,

%e a(20) = x(20) + 20*y(20) = 4 + 20*2 = 44.

%o (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 Cf. A000925, A283305, A283306, A304584, A304585.

%K nonn

%O 0,3

%A _Hugo Pfoertner_, Jun 15 2018