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A366354
a(0) = 0; for n > 0, a(n) is the largest taxicab distance on a square spiral between any two previous occurrences of a(n-1). If a(n-1) has not previously occurred then a(n) = 0.
4
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, 4, 8, 8, 9, 0, 10, 0, 10, 2, 7, 8, 12, 0, 10, 8, 12, 4, 8, 12, 7, 8, 12, 10, 9, 6, 12, 12, 12, 12, 12, 12, 12, 13, 0, 11, 0, 11, 2, 8, 12, 14, 0, 11, 8, 12, 14, 5, 8, 12, 15, 0, 15, 2, 9, 10, 9, 10, 11
OFFSET
0,5
LINKS
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:
.
.
0---9---8---8---4---5---8 :
| | :
10 6---0---5---2---4 4 10
| | | | |
0 0 2---0---1 0 5 12
| | | | | | |
10 6 0 0---0 4 7 8
| | | | | |
2 2 2---2---3---0 0 7
| | | |
7 6---4---7---0---6---8 12
| |
8--12---0--10---8--12---4---8
.
a(2) = 1 as the maximum taxicab distance between 0 = a(1) and the only previous occurrence of 0, a(0) at (0,0), is 1.
a(8) = 3 as the maximum taxicab distance between any two previous occurrences of 2 = a(7) is 3, between a(3) = 2, at (-1,1) relative to the starting square, and a(7) = 2 at (0,-1) relative to the starting square.
a(32) = 4 as the maximum taxicab distance between any two previous occurrences of 5 = a(31) is 4, between a(14) = 5, at (0,2) relative to the starting square, and a(28) = 5 at (3,1) relative to the starting square. This is the first term to differ from A366353.
CROSSREFS
Sequence in context: A334203 A309107 A366353 * A144741 A352965 A103615
KEYWORD
nonn
AUTHOR
Scott R. Shannon, Oct 08 2023
STATUS
approved