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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 (list; graph; refs; listen; history; text; internal format)
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

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

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Last modified September 18 23:16 EDT 2021. Contains 347548 sequences. (Running on oeis4.)