A393465 The grid points at integer Euclidean distance from the central point of an infinite square spiral.

1, 2, 4, 6, 8, 11, 15, 19, 23, 28, 34, 40, 46, 50, 53, 56, 58, 61, 64, 66, 69, 72, 74, 77, 80, 86, 96, 106, 116, 127, 139, 151, 163, 176, 190, 204, 218, 227, 233, 239, 243, 249, 255, 259, 265, 271, 275, 281, 287, 298, 316, 334, 352, 371, 391, 411, 431, 452

Offset

1,2

Comments

Equivalently, numbers k such that A336336(k) = A174344(k)^2 + A274923(k)^2 is a square number.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Rémy Sigrist, PARI program

Example

The first terms, alongside the square spiral, are:
      .--.--.--.--.-96--.--.--.--.--.
      |                             |
      .  .-64--.--.-61--.--.-58--.  .
      |  |                       |  |
      . 66  .--.--.-34--.--.--. 56  .
      |  |  |                 |  |  |
      .  .  .  .--.-15--.--.  .  .  .
      |  |  |  |           |  |  |  |
      .  .  .  .  .--4--.  .  .  .  .
      |  |  |  |  |     |  |  |  |  |
    106 69 40 19  6  1--2 11 28 53 86
      |  |  |  |  |        |  |  |  |
      .  .  .  .  .--8--.--.  .  .  .
      |  |  |  |              |  |  |
      .  .  .  .--.-23--.--.--.  .  .
      |  |  |                    |  |
      . 72  .--.--.-46--.--.--.-50  .
      |  |                          |
      .  .-74--.--.-77--.--.-80--.--.
      |
      .--.--.--.--.116--.--.--.--.--.

Prog

(PARI) \\ See Links section.

Crossrefs

Cf. A174344, A274923, A331400, A336336, A393466 (corresponding distances).

Sequence in context: A374263 A338237 A385174 * A039823 A284617 A079972

Adjacent sequences: A393462 A393463 A393464 * A393466 A393467 A393468

Keyword

nonn

Author

Rémy Sigrist, Feb 15 2026

Status

approved