A365344 a(0) = 0; for n > 0, a(n) is the largest distance squared on a square spiral between a(n-1) and any previous occurrence of a(n-1). If a(n-1) has not previously occurred then a(n) = 0.

0, 0, 1, 0, 2, 0, 4, 0, 4, 4, 9, 0, 10, 0, 10, 4, 18, 0, 16, 0, 20, 0, 20, 4, 20, 16, 29, 0, 26, 0, 34, 0, 34, 4, 26, 20, 41, 0, 40, 0, 40, 4, 34, 72, 0, 45, 0, 41, 61, 0, 74, 0, 58, 0, 50, 0, 61, 50, 5, 0, 58, 32, 0, 85, 0, 113, 0, 89, 0, 73, 0, 89, 16, 53, 0, 85, 68, 0, 89, 61, 65, 0, 145, 0

Offset

0,5

Links

Scott R. Shannon, Table of n, a(n) for n = 0..10000

Example

The spiral begins:
.
  41--20--26--4---34--0---34  .
  |                       |   .
  0   18--4---10--0---10  0   50
  |   |               |   |   |
  40  0   2---0---1   0   26  0
  |   |   |       |   |   |   |
  0   16  0   0---0   9   0   58
  |   |   |           |   |   |
  40  0   4---0---4---4   29  0
  |   |                   |   |
  4   20--0---20--4---20--16  74
  |                           |
  34--72--0---45--0---41--61--0
.
.
a(4) = 2 as a(3) = 0 and the largest square distance between a(3) and a previous occurrence of 0 is 2 - between a(3) and a(1).
a(47) = 41 as a(46) = 0 and the largest square distance between a(46) and a previous occurrence of 0 is 41 - between a(46) and a(37). This is the first term to differ from A365343.

Crossrefs

Cf. A366543, A366353, A366354, A001481.

Sequence in context: A337599 A322337 A211008 * A366543 A286663 A114402

Adjacent sequences: A365341 A365342 A365343 * A365345 A365346 A365347

Keyword

nonn

Author

Scott R. Shannon, Oct 16 2023

Status

approved