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%I #16 Oct 20 2023 01:51:39
%S 0,0,1,0,2,0,2,0,3,0,3,1,1,2,2,3,2,2,5,0,3,2,4,0,5,0,4,1,3,3,4,1,3,4,
%T 1,3,5,1,4,1,5,2,5,2,6,0,4,2,7,0,4,5,4,4,5,3,6,1,5,3,5,4,9,0,4,6,1,8,
%U 0,9,1,7,0,10,0,10,0,9,2,7,2,6,3,6,3,6,1,7,2,9,1,7,3,6,4,7,2,8,0
%N a(0) = 0; for n > 0, a(n) is the total number of other numbers, being constructed on a square spiral, that are visible from a(n-1) that equal a(n-1).
%C A number is visible from any given number if, given that it has coordinates (x,y) relative to that number, the greatest common divisor of |x| and |y| is 1.
%H Scott R. Shannon, <a href="/A363824/b363824.txt">Table of n, a(n) for n = 0..10000</a>
%H Scott R. Shannon, <a href="/A363824/a363824_1.png">Image of the first 500000 terms</a>.
%H Scott R. Shannon, <a href="/A363824/a363824.png">Image of the first 10000 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 The spiral begins:
%e .
%e .
%e 5---3---1---4---3---1---4 :
%e | | :
%e 1 2---3---2---2---1 3 5
%e | | | | |
%e 4 2 2---0---1 1 3 4
%e | | | | | | |
%e 1 5 0 0---0 3 1 4
%e | | | | | |
%e 5 0 2---0---3---0 4 5
%e | | | |
%e 2 3---2---4---0---5---0 4
%e | |
%e 5---2---6---0---4---2---7---0
%e .
%e a(1) = 0 as a(0) = 0, and there are currently no other numbers that equal 0.
%e a(2) = 1 as a(1) = 0, and from a(1), at (1,0) relative to the starting square, there is currently one other visible 0, namely a(0).
%e a(6) = 2 as a(5) = 0, and from a(5), at (-1,0) relative to the starting square, there are currently two other visible 0's, namely a(0) and a(3). Note that a(1) = 0 is not visible as it is hidden by a(0).
%Y Cf. A331400, A357991, A357985, A347358, A347357.
%K nonn,look
%O 0,5
%A _Scott R. Shannon_, Oct 19 2023