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 A270558 Area of the smallest convex n-gon such that all its sides, diagonals and area are distinct integers. 0
 6, 378, 9870, 196950, 5695998, 12473070 (list; graph; refs; listen; history; text; internal format)
 OFFSET 3,1 COMMENTS Does such an n-gon exist for all n >= 3? - Dmitry Kamenetsky, Feb 15 2017 LINKS Carlos Rivera, Problem 64: prime convex quadrilateral. Carlos Rivera, Problem 65: prime convex polygons. EXAMPLE For n=3, we have the triangle with sides 3, 4 and 5. Its area is 6. For n=4, we have the quadrilateral with sides 10, 17, 28, 35, diagonals 21 and 39, and area 378. For n=5, we have the 5-gon with sides 21, 41, 175, 140, 85, diagonals 50, 105, 104, 204, 195, and area 9870. For n=6, we have the 6-gon with sides 47, 663, 264, 169, 105, 1020, diagonals 700, 884, 975, 855, 952, 1001, 425, 520, 272, and area 196950. For n=7, we have the 7-gon with sides 235, 1320, 1360, 2340, 612, 525, 5100, diagonals 1547, 2805, 4557, 4875, 2600, 4420, 4760, 5005, 3500, 3952, 4301, 2880, 3315, 1131, and area 5695998. For n=8, we have the 8-gon with sides 1547, 612, 525, 5355, 235, 4275, 845, 1360, diagonals 2125, 2600, 5365, 5304, 2163, 1131, 5520, 5525, 3500, 2805, 5460, 5491, 3952, 3315, 5408, 4301, 3720, 4420, 4875, 4760, and area 12473070. See the Rivera links for images of these. CROSSREFS Sequence in context: A099595 A158041 A233212 * A245398 A078207 A261296 Adjacent sequences:  A270555 A270556 A270557 * A270559 A270560 A270561 KEYWORD nonn,more AUTHOR Dmitry Kamenetsky, Mar 18 2016 EXTENSIONS a(6)-a(8) from Luca Petrone, Feb 06 2017 STATUS approved

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Last modified February 27 09:44 EST 2020. Contains 332301 sequences. (Running on oeis4.)