%I #14 Apr 12 2020 13:58:23

%S 1,2,3,5,6,7,10,11,13,14,17,18,20,21,26,27,30,31,37,38,41,43,44,46,50,

%T 52,55,57,58,65,66,70,73,79,82,83,88,91,92,101,102,104,110,111,116,

%U 122,124,127,132,133,141,143,145,146,152,156,157,167,170,171,180

%N Lexicographically earliest sequence of distinct positive integers, which when mapped onto a square spiral, gives a set without four distinct points forming a square.

%C This sequence has similarities with A005282.

%H Rémy Sigrist, <a href="/A333866/b333866.txt">Table of n, a(n) for n = 1..10000</a>

%H Rémy Sigrist, <a href="/A333866/a333866.png">Scatterplot of (A174344(a(n)), A274923(a(n))) in the region -2000 <= x, y <= 2000</a>

%H Rémy Sigrist, <a href="/A333866/a333866.txt">C# program for A333866</a>

%e The first terms, mapped onto a square spiral, are:

%e 65---*---*---*---*---*---*--58--57

%e | |

%e 66 37---*---*---*---*---*--31 *

%e | | | |

%e * 38 17---*---*--14--13 30 55

%e | | | | | |

%e * * 18 5---*---3 * * * <-- As the sequence contains 2, 13

%e | | | | | | | | and 27, it cannot contain 54.

%e * * * 6 1---2 11 * *

%e | | | | | | |

%e 70 41 20 7---*---*--10 27 52

%e | | | | |

%e * * 21---*---*---*---*--26 *

%e | | |

%e * 43--44---*--46---*---*---*--50

%e |

%e 73---*---*---*---*---*--79---*---*

%o (C#) See Links section.

%Y See A333825 for a similar sequences.

%Y Cf. A005282, A174344, A274923.

%K nonn

%O 1,2

%A _Rémy Sigrist_, Apr 08 2020