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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

Table of n, a(n) for n=3..8.

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 July 22 22:25 EDT 2017. Contains 289676 sequences.