A198311 Minimum perimeter of n-tuples of Heronian triangles with equal perimeter and equal area.

12, 70, 98, 448, 1170, 2340, 11700, 84630, 94668, 428736, 662676, 1325352

Offset

1,1

Comments

Kurz's paper reports the first 10 values in a table on page 193, but for some reason the areas are multiplied by 4 (A204559) and the last two values are incorrect since correspond to n-tuples which are not minimal.

If n-tuples were sorted by area instead, a(2) would have been 84, corresponding to triangles (10, 35, 39), (14, 30, 40) with common minimal area 168.

Links

Table of n, a(n) for n=1..12.

Sascha Kurz, On the generation of Heronian triangles, Serdica Journal of Computing Vol. 2 (2008), 181-196.

Giovanni Resta, n-tuples for n=1..12

Example

The first 3 entries and corresponding triangles:
a(1) = p = 12, A = 6, T = (3, 4, 5);
a(2) = p = 70, A = 210, T = (17, 25, 28), (20, 21, 29);
a(3) = p = 98, A = 420, T = (24, 37, 37), (25, 34, 39), (29, 29, 40).

Crossrefs

Cf. A204559, A334285.

Sequence in context: A163193 A088832 A366748 * A379264 A374977 A060930

Adjacent sequences: A198308 A198309 A198310 * A198312 A198313 A198314

Keyword

nonn,hard,more

Author

Peter Luschny, Jan 21 2012

Extensions

a(9)-a(10) corrected and a(11)-a(12) added by Giovanni Resta, Apr 21 2020

Status

approved