A334752 a(n) is the number immediately below n in a clockwise square spiral of the positive integers with the first step to the right.

4, 3, 14, 15, 16, 5, 6, 1, 2, 11, 12, 13, 32, 33, 34, 35, 36, 17, 18, 19, 20, 7, 8, 9, 10, 27, 28, 29, 30, 31, 58, 59, 60, 61, 62, 63, 64, 37, 38, 39, 40, 41, 42, 21, 22, 23, 24, 25, 26, 51, 52, 53, 54, 55, 56, 57, 92, 93, 94, 95, 96, 97, 98, 99, 100, 65, 66

Offset

1,1

Comments

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

This is a permutation of the positive integers. A334751 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) = 4 because 4 is immediately below 1 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), A334751 (above).

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

Sequence in context: A056479 A056480 A284841 * A197883 A222195 A292413

Adjacent sequences: A334749 A334750 A334751 * A334753 A334754 A334755

Keyword

nonn

Author

Peter Kagey, May 10 2020

Status

approved