

A289523


Lexicographically earliest sequence of positive integers such that no circles centered at (n, a(n)) with radius sqrt(n) overlap.


1



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, 1, 51, 95, 34, 62, 106, 10, 79, 117, 129, 21, 43, 141, 90, 1, 55, 68, 103, 31, 152, 13, 116, 80, 130, 165, 43, 180, 195, 1, 57, 92, 23, 142, 107, 209, 71, 225, 123
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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 ycoordinate 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 n1 do
if (in)^2 <= i+n or 4*n*i > ((in)^2  (n+i))^2 then
r:= ceil(sqrt((sqrt(n)+sqrt(i))^2  (ni)^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

Sequence in context: A082169 A209634 A340584 * A078220 A256040 A257817
Adjacent sequences: A289520 A289521 A289522 * A289524 A289525 A289526


KEYWORD

nonn


AUTHOR

Peter Kagey, Jul 07 2017


STATUS

approved



