|
%I #18 May 01 2020 08:11:11
%S 12,70,98,448,1170,2340,11700,84630,94668,428736,662676,1325352
%N Minimum perimeter of n-tuples of Heronian triangles with equal perimeter and equal area.
%C 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.
%C 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.
%H Sascha Kurz, <a href="http://serdica-comp.math.bas.bg/index.php/serdicajcomputing/article/view/48">On the generation of Heronian triangles</a>, Serdica Journal of Computing Vol. 2 (2008), 181-196.
%H Giovanni Resta, <a href="/A198311/a198311.txt">n-tuples for n=1..12</a>
%e The first 3 entries and corresponding triangles:
%e a(1) = p = 12, A = 6, T = (3, 4, 5);
%e a(2) = p = 70, A = 210, T = (17, 25, 28), (20, 21, 29);
%e a(3) = p = 98, A = 420, T = (24, 37, 37), (25, 34, 39), (29, 29, 40).
%Y Cf. A204559, A334285.
%K nonn,hard,more
%O 1,1
%A _Peter Luschny_, Jan 21 2012
%E a(9)-a(10) corrected and a(11)-a(12) added by _Giovanni Resta_, Apr 21 2020
|
