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

1,2

Links

Kevin Ryde, Table of n, a(n) for n = 1..10000

Index entries for sequences that are permutations of the natural numbers

Formula

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

Example

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
.

Crossrefs

Cf. A102083.

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

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

Sequence in context: A076696 A011057 A082236 * A362269 A262027 A328487

Adjacent sequences: A337819 A337820 A337821 * A337823 A337824 A337825

Keyword

nonn

Author

Mohammed Yaseen, Sep 24 2020

Status

approved