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A141247 Minimum number of points visible from a point in a square n X n lattice. 2


%S 1,4,6,10,14,22,26,38,46,58,66,86,94,118,130,146,162,194,206,241,257,

%T 282,302,346,362,401,426,462,486,542,558,609,641,690,722,770,794,861,

%U 899,950,982,1062,1086,1157,1201,1258,1302,1393,1425,1501,1546,1613

%N Minimum number of points visible from a point in a square n X n lattice.

%C Two points (a,b) and (c,d) are visible to each other when gcd(c-a,d-b)=1. Sequence A141248 gives the number of lattice points that have minimal visibility.

%H T. D. Noe, <a href="/A141247/b141247.txt">Table of n, a(n) for n=1..1000</a>

%H Eric Weisstein, <a href="http://mathworld.wolfram.com/VisiblePoint.html">MathWorld: Visible Point</a>

%F The minimum number of visible points is slightly less than c*n^2, with c = 6/pi^2.

%t Table[mn=n^2+1; Do[cnt=0; Do[If[GCD[c-a,d-b]<2, cnt++ ], {a,n}, {b,n}]; If[cnt<mn, mn=cnt], {c,n}, {d,n}]; mn, {n,20}]

%Y Cf. A141224.

%K nonn

%O 1,2

%A _T. D. Noe_, Jun 17 2008

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Last modified September 23 08:23 EDT 2021. Contains 347610 sequences. (Running on oeis4.)