A334751 a(n) is the number immediately above n in a clockwise square spiral of the positive integers with the first step to the right.

8, 9, 2, 1, 6, 7, 22, 23, 24, 25, 10, 11, 12, 3, 4, 5, 18, 19, 20, 21, 44, 45, 46, 47, 48, 49, 26, 27, 28, 29, 30, 13, 14, 15, 16, 17, 38, 39, 40, 41, 42, 43, 74, 75, 76, 77, 78, 79, 80, 81, 50, 51, 52, 53, 54, 55, 56, 31, 32, 33, 34, 35, 36, 37, 66, 67, 68, 69

Offset

1,1

Comments

Equivalently the number immediately below n in a counterclockwise spiral of the positive integers with the first step to the right.

This is a permutation of the positive integers. A334752 is the inverse permutation.

Links

Peter Kagey, Table of n, a(n) for n = 1..10000

Index entries for sequences that are permutations of the natural numbers

Example

For n = 1, a(1) = 8 because 8 is immediately above one in the clockwise square spiral with first step to the right:
  21--22--23--24--25--26
  |                    |
  20  7---8---9---10  27
  |   |            |   |
  19  6   1---2   11  28
  |   |       |    |   |
  18  5---4---3   12  29
  |                |   |
  17--16--15--14--13  30
                       |
  36--35--34--33--32--31

Crossrefs

Cf. A068225 (right), A068226 (left), A334752 (below).

Cf. A174344 (x-coordinate), A268038 (y-coordinate).

Sequence in context: A297537 A030167 A010767 * A289252 A064734 A090929

Adjacent sequences: A334748 A334749 A334750 * A334752 A334753 A334754

Keyword

nonn

Author

Peter Kagey, May 10 2020

Status

approved