Search: a001481 -id:a001481
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A366153
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Starting with the n-th shortest Cartesian line segment, a(n) is the minimal number of consecutive line segments required to make a simple polygon.
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+10
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4, 5, 4, 3, 4, 3, 4, 4, 5, 4, 5, 4, 4, 6, 5, 6, 5, 6, 5, 7, 6, 4, 5, 5, 4, 4, 5
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OFFSET
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1,1
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COMMENTS
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List the possible lengths of line segments achievable by connecting integral coordinates on a Cartesian grid. Starting from the n-th length, a(n) is the smallest number of consecutively greater lengths required to form a simple polygon with all vertices on integral Cartesian coordinates.
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LINKS
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EXAMPLE
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a(4) = 3 because i) the fourth, fifth and sixth lengths are sqrt(5), sqrt(8) and 3 and ii) a triangle can be created using edges with these three lengths.
a(5) = 4 because i) the fifth, sixth, seventh and eighth lengths are sqrt(8), 3, sqrt(10), sqrt(13) and ii) a quadrilateral can be created using edges with these four lengths and iii) the fifth, sixth and seventh lengths alone cannot create a simple polygon with integral Cartesian vertices.
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CROSSREFS
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Cf. A001481 (List of the squares of possible line segment lengths with both endpoints integral Cartesian coordinates).
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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