OFFSET
1,2
LINKS
Peter Kagey, Table of n, a(n) for n = 1..3000
Peter Kagey, Plot of the first 500 circles
EXAMPLE
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.
MAPLE
A[1]:= 1:
for n from 2 to 100 do
excl:= {}:
for i from 1 to n-1 do
if (i-n)^2 <= i+n or 4*n*i > ((i-n)^2 - (n+i))^2 then
r:= ceil(sqrt((sqrt(n)+sqrt(i))^2 - (n-i)^2))-1;
excl:= excl union {$(A[i]-r) .. (A[i]+r)};
fi
od;
A[n]:= min({$1..max(excl)+1} minus excl);
od:
seq(A[i], i=1..100); # Robert Israel, Jul 07 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Peter Kagey, Jul 07 2017
STATUS
approved