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Search: id:A141227
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| A141227 |
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Maximum number of points visible from some point in a cubic n x n x n lattice. |
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+0
2
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| 1, 8, 27, 57, 111, 183, 303, 435, 633, 843, 1155, 1443, 1893, 2313, 2895, 3447, 4215, 4875, 5865, 6723, 7887, 8943, 10371, 11553, 13293, 14745, 16707, 18411, 20703, 22485, 25257, 27459, 30423, 32931, 36291, 38889, 42837, 45950, 50115, 53523
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Two points (a,b,c) and (d,e,f) are visible to each other when gcd(d-a,e-b,f-c)=1. Sequence A141228 gives the number of lattice points that have maximal visibility.
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LINKS
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Eric Weisstein, MathWorld: Visible Point
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FORMULA
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The maximum number of visible points is slightly more than c*n^3, with c = 1/zeta(3) = 0.831907... (A088453).
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MATHEMATICA
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Table[mx=0; Do[cnt=0; Do[If[GCD[d-a, e-b, f-c]<2, cnt++ ], {a, n}, {b, n}, {c, n}]; If[cnt>mx, mx=cnt], {d, n}, {e, n}, {f, n}]; mx, {n, 10}]
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CROSSREFS
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Cf. A141224.
Sequence in context: A063144 A122013 A131620 this_sequence A151675 A062686 A093322
Adjacent sequences: A141224 A141225 A141226 this_sequence A141228 A141229 A141230
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KEYWORD
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nonn
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AUTHOR
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T. D. Noe (noe(AT)sspectra.com), Jun 15 2008
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