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%I #12 Jul 08 2017 00:48:34
%S 1,4,7,1,11,16,5,21,27,34,10,1,41,17,49,25,57,6,33,66,43,14,75,85,24,
%T 1,51,95,34,62,106,10,79,117,129,21,43,141,90,1,55,68,103,31,152,13,
%U 116,80,130,165,43,180,195,1,57,92,23,142,107,209,71,225,123
%N Lexicographically earliest sequence of positive integers such that no circles centered at (n, a(n)) with radius sqrt(n) overlap.
%H Peter Kagey, <a href="/A289523/b289523.txt">Table of n, a(n) for n = 1..3000</a>
%H Peter Kagey, <a href="/A289523/a289523_1.png">Plot of the first 500 circles</a>
%e For n = 3, a(3) = 7 because a circle centered at (3, 1) with radius sqrt(3) intersects the circle centered at (1, 1) with radius sqrt(1); a circle centered at (3, k) with radius sqrt(3) intersects the circle centered at (2, 4) with radius sqrt(2), for 2 <= k <= 6; therefore the circle centered at (3, 7) is the circle with the least y-coordinate that does not intersect any of the existing circles.
%p A[1]:= 1:
%p for n from 2 to 100 do
%p excl:= {}:
%p for i from 1 to n-1 do
%p if (i-n)^2 <= i+n or 4*n*i > ((i-n)^2 - (n+i))^2 then
%p r:= ceil(sqrt((sqrt(n)+sqrt(i))^2 - (n-i)^2))-1;
%p excl:= excl union {$(A[i]-r) .. (A[i]+r)};
%p fi
%p od;
%p A[n]:= min({$1..max(excl)+1} minus excl);
%p od:
%p seq(A[i],i=1..100); # _Robert Israel_, Jul 07 2017
%K nonn
%O 1,2
%A _Peter Kagey_, Jul 07 2017
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