Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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