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A366543 a(0) = 0; for n > 0, a(n) is the largest distance squared 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 A366543 #27 Feb 12 2024 08:38:31
%S A366543 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,
%T A366543 0,34,0,34,4,26,20,41,0,40,0,40,4,34,72,0,45,0,45,4,45,16,40,53,0,50,
%U A366543 0,61,0,65,0,65,4,65,16,85,0,68,0,68,4,65,72,4,73,0,89,0,89,4,73,36,0,130,0
%N A366543 a(0) = 0; for n > 0, a(n) is the largest distance squared 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 A366543 Scott R. Shannon, <a href="/A366543/b366543.txt">Table of n, a(n) for n = 0..10000</a>
%e A366543 The spiral begins:
%e A366543 ..
%e A366543   41--20--26--4---34--0---34  .
%e A366543   |                       |   .
%e A366543   0   18--4---10--0---10  0   50
%e A366543   |   |               |   |   |
%e A366543   40  0   2---0---1   0   26  0
%e A366543   |   |   |       |   |   |   |
%e A366543   0   16  0   0---0   9   0   53
%e A366543   |   |   |           |   |   |
%e A366543   40  0   4---0---4---4   29  40
%e A366543   |   |                   |   |
%e A366543   4   20--0---20--4---20--16  16
%e A366543   |                           |
%e A366543   34--72--0---45--0---45--4---45
%e A366543 .
%e A366543 .
%e A366543 a(4) = 2 as a(3) = 0 and the largest square distance between any previous pairs of 0's is 2 - between a(3) and a(1).
%e A366543 a(47) = 45 as a(46) = 0 and the largest square distance between any previous pairs of 0's is 45 - between a(44) and a(31). This is the first term to differ from A365344.
%Y A366543 Cf. A365344, A366353, A366354, A001481.
%K A366543 nonn
%O A366543 0,5
%A A366543 _Scott R. Shannon_, Oct 16 2023