A098030 Areas of integer-sided triangles whose area equals their perimeter.

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

Table of n, a(n) for n=1..5.

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

Adjacent sequences: A098027 A098028 A098029 * A098031 A098032 A098033

Keyword

fini,full,nonn

Author

Lekraj Beedassy, Sep 10 2004

Status

approved