A337822 Permutation of the natural numbers formed by numbering an infinite square grid by a counterclockwise diamond spiral and visiting them by a counterclockwise stair step spiral.

1, 2, 8, 3, 9, 20, 10, 21, 11, 4, 12, 5, 13, 14, 6, 15, 7, 16, 30, 17, 31, 18, 32, 19, 33, 52, 34, 53, 35, 54, 36, 55, 37, 22, 38, 23, 39, 24, 40, 25, 41, 42, 26, 43, 27, 44, 28, 45, 29, 46, 68, 47, 69, 48, 70, 49, 71, 50, 72, 51, 73, 100, 74, 101, 75, 102, 76

Offset: 1

Author

Mohammed Yaseen, Sep 24 2020

Keywords

• nonn

Examples

			The path begins:
.
               ---33
                   |
              34  19--32
                       |
          35  20---9  18--31  48
               |   |       |
      36  21--10   3---8  17--30  47
           |           |       |
  37  22  11---4   1---2   7--16  29  46
               |           |
      38  23  12---5   6--15  28  45
                   |   |
          39  24  13--14  27  44
.
              40  25  26  43
.
                  41  42
.
		

Links

• Kevin Ryde, Table of n, a(n) for n = 1..10000
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A102083.

Diamond spiral coordinates (but 0-based): A010751, A305258.

Same type of visit on other types of spirals: A334619, A337838.

Formula

a(A102083(n)) = A102083(n) and a(A102083(n)+1) = A102083(n)+1.