A333866 Lexicographically earliest sequence of distinct positive integers, which when mapped onto a square spiral, gives a set without four distinct points forming a square.

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, 52, 55, 57, 58, 65, 66, 70, 73, 79, 82, 83, 88, 91, 92, 101, 102, 104, 110, 111, 116, 122, 124, 127, 132, 133, 141, 143, 145, 146, 152, 156, 157, 167, 170, 171, 180

Offset: 1

Author

Rémy Sigrist, Apr 08 2020

Keywords

• nonn

Comments

This sequence has similarities with A005282.

Examples

			The first terms, mapped onto a square spiral, are:
        65---*---*---*---*---*---*--58--57
         |                               |
        66  37---*---*---*---*---*--31   *
         |   |                       |   |
         *  38  17---*---*--14--13  30  55
         |   |   |               |   |   |
         *   *  18   5---*---3   *   *   * <-- As the sequence contains 2, 13
         |   |   |   |       |   |   |   |     and 27, it cannot contain 54.
         *   *   *   6   1---2  11   *   *
         |   |   |   |           |   |   |
        70  41  20   7---*---*--10  27  52
         |   |   |                   |   |
         *   *  21---*---*---*---*--26   *
         |   |                           |
         *  43--44---*--46---*---*---*--50
         |
        73---*---*---*---*---*--79---*---*
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000
• Rémy Sigrist, Scatterplot of (A174344(a(n)), A274923(a(n))) in the region -2000 <= x, y <= 2000
• Rémy Sigrist, C# program for A333866

Crossrefs

See A333825 for a similar sequences.

Cf. A005282, A174344, A274923.