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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.

%I A366354 #12 Oct 16 2023 13:42:50
%S A366354 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,
%T A366354 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,
%U A366354 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
%N 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.
%H A366354 Scott R. Shannon, <a href="/A366354/b366354.txt">Table of n, a(n) for n = 0..10000</a>
%H A366354 Scott R. Shannon, <a href="/A366354/a366354_1.png">Image of the first 500000 terms</a>.
%H A366354 Scott R. Shannon, <a href="/A366354/a366354.png">Image of the first 50000 terms on the square spiral</a>. The colors are graduated across the spectrum to show their relative size. Zoom in to see the numbers.
%e A366354 The spiral begins:
%e A366354 .
%e A366354                                 .
%e A366354     0---9---8---8---4---5---8   :
%e A366354     |                       |   :
%e A366354    10   6---0---5---2---4   4   10
%e A366354     |   |               |   |   |
%e A366354     0   0   2---0---1   0   5   12
%e A366354     |   |   |       |   |   |   |
%e A366354    10   6   0   0---0   4   7   8
%e A366354     |   |   |           |   |   |
%e A366354     2   2   2---2---3---0   0   7
%e A366354     |   |                   |   |
%e A366354     7   6---4---7---0---6---8   12
%e A366354     |                           |
%e A366354     8--12---0--10---8--12---4---8
%e A366354 .
%e A366354 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.
%e A366354 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.
%e A366354 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.
%Y A366354 Cf. A366353, A214526.
%K A366354 nonn
%O A366354 0,5
%A A366354 _Scott R. Shannon_, Oct 08 2023