A366353 a(0) = 0; for n > 0, a(n) is the largest taxicab distance 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, 2, 2, 3, 0, 4, 0, 4, 2, 5, 0, 6, 0, 6, 2, 6, 4, 7, 0, 6, 8, 0, 7, 5, 4, 8, 5, 3, 4, 6, 8, 10, 0, 9, 0, 7, 7, 8, 12, 0, 7, 6, 8, 10, 12, 6, 10, 11, 0, 9, 8, 13, 0, 11, 6, 9, 6, 11, 10, 13, 8, 12, 13, 11, 10, 9, 12, 8, 15, 0, 13, 13, 12, 11, 12, 13, 16, 0, 13, 15, 11, 11, 10, 12

Offset

0,5

Links

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

Scott R. Shannon, Image of the first 500000 terms.

Scott R. Shannon, Image of the first 50000 terms on the square spiral. The colors are graduated across the spectrum to show their relative size. Zoom in to see the numbers.

Example

The spiral begins:
.
                                .
    10--8---6---4---3---5---8   :
    |                       |   :
    0   6---0---5---2---4   4   9
    |   |               |   |   |
    9   0   2---0---1   0   5   0
    |   |   |       |   |   |   |
    0   6   0   0---0   4   7   11
    |   |   |           |   |   |
    7   2   2---2---3---0   0   10
    |   |                   |   |
    7   6---4---7---0---6---8   6
    |                           |
    8---12--0---7---6---8---10--12
.
a(2) = 1 as the taxicab distance between a(1) = 0, at (1,0) relative to the starting square, and the only previous occurrence of 0, a(0) at (0,0), is 1.
a(8) = 3 as the maximum taxicab distance between a(7) = 2, at (0,-1) relative to the starting square, and any previous occurrence of 2 is 3, to a(4) = 2 at (-1,1) relative to the starting square.
a(32) = 3 as the maximum taxicab distance between a(31) = 5, at (2,3) relative to the starting square, and any previous occurrence of 5 is 3, to a(28) = 5 at (3,1) relative to the starting square, and also to a(14) = 5 at (0,2) relative to the starting square. This is the first term to differ from A366354.

Crossrefs

Cf. A366354, A214526.

Sequence in context: A334203 A394974 A309107 * A366354 A144741 A352965

Adjacent sequences: A366350 A366351 A366352 * A366354 A366355 A366356

Keyword

nonn

Author

Scott R. Shannon, Oct 08 2023

Status

approved