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A098030
Areas of integer-sided triangles whose area equals their perimeter.
13
24, 30, 36, 42, 60
OFFSET
1,1
COMMENTS
There are no further terms. Note that without the condition "integer-sided" there are other solutions, such as (9/2, 20, 41/2) which has perimeter and area 45. - David Wasserman, Jan 03 2008
REFERENCES
S. Ainley, Mathematical Puzzles, Problem J8 p. 113, G. Bell & Sons Ltd, London (1977).
LINKS
James Grime and Brady Haran, Superhero Triangles, Numberphile video (2020)
EXAMPLE
The areas or perimeters 24, 30, 36, 42, 60 pertain respectively to triangles with sides (6, 8, 10), (5, 12, 13), (9, 10, 17), (7, 15, 20), (6, 25, 29).
MATHEMATICA
m0 = 10 (* = initial max side *); okQ[{x_, y_, z_}] := x <= y <= z && (-x + y + z) (x + y - z) (x - y + z) (x + y + z) == 16 (x + y + z)^2; Clear[f];
f[m_] := f[m] = Select[Tuples[Range[m], 3], okQ]; f[m = m0]; f[m = 2 m]; While[f[m] != f[m/2], m = 2 m]; sides = f[m]; Total /@ sides // Sort (* Jean-François Alcover, Jul 21 2017 *)
CROSSREFS
A row of the triangle in A290451.
Sequence in context: A248693 A075422 A230195 * A290451 A068544 A284174
KEYWORD
fini,full,nonn
AUTHOR
Lekraj Beedassy, Sep 10 2004
STATUS
approved