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

Author

Peter Kagey, May 10 2020

Keywords

• nonn

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.

Examples

			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
		

Links

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

Crossrefs

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

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