A333825 -id:A333825 - cp's OEIS frontend

A333835 Lexicographically earliest sequence of distinct positive integers, which when mapped onto a square spiral, gives a set without three distinct evenly spaced aligned points.

1, 2, 3, 4, 17, 18, 20, 21, 22, 24, 27, 28, 31, 33, 34, 61, 80, 81, 87, 90, 93, 100, 131, 135, 145, 146, 148, 152, 154, 157, 158, 160, 166, 171, 172, 174, 189, 194, 225, 253, 268, 270, 271, 276, 281, 282, 291, 294, 295, 298, 316, 335, 338, 368, 383, 397, 405

Offset: 1

Rémy Sigrist, Apr 07 2020

nonn

This sequence has similarities with A005836 and A229037.

			The first terms, mapped onto a square spiral, are:
         *---*---*---*--61---*---*---*---*
         |                               |
         *   *---*---*--34--33---*--31   *
         |   |                       |   |
         *   *  17---*---*---*---*   *   *
         |   |   |               |   |   |
         *   *  18   *---4---3   *   *   *
         |   |   |   |       |   |   |   |
         *   *   *   *   1---2   *  28   *
         |   |   |   |           |   |   |
         *   *  20   *---*---*---*  27   *
         |   |   |                   |   |
         *   *  21--22---*--24---*---*   *
         |   |                           |
         *   *---*---*---*---*---*---*---*
         |
         *---*---*---*---*---*---*--80--81

Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, Scatterplot of (A174344(a(n)), A274923(a(n))) in the region -10000 <= x, y <= 10000
Rémy Sigrist, C# program for A333835

See A333825 for a similar sequences.

Cf. A005836, A174344, A229037, A274923.

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.

Original entry on oeis.org

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

Rémy Sigrist, Apr 08 2020

nonn

This sequence has similarities with A005282.

			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---*---*

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

See A333825 for a similar sequences.

Cf. A005282, A174344, A274923.

cp's OEIS Frontend

A333835 Lexicographically earliest sequence of distinct positive integers, which when mapped onto a square spiral, gives a set without three distinct evenly spaced aligned points.

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