login
Sides of integer Heronian triangles [prime(A068964(n)), prime(A068964(n)+1), a(n)] with area A068966(n).
3

%I #16 Apr 20 2020 12:57:48

%S 4,20,170,452,890,2180,4052,5210,6500,10100,27380,43220,84068,95930,

%T 118100,130052,183620,198458,246410,281252,357860,399620,410420,

%U 455060,581060,656660,900500,1022468,1134020,1188890,1232468,1401140,1462058,1545290,1609220,1630820

%N Sides of integer Heronian triangles [prime(A068964(n)), prime(A068964(n)+1), a(n)] with area A068966(n).

%H Giovanni Resta, <a href="/A068965/b068965.txt">Table of n, a(n) for n = 1..385</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HeronianTriangle.html">Heronian Triangle</a>.

%e A068964(3) = 24: [A000040(24), A000040(25), a(3)] = [89,97,170], with s = (89+97+170)/2 = 178: Area^2 = s*(s-89)*(s-81)*(s-170) = 178*89*81*8 = 10265616 = 3204*3204, therefore A068966(3) = 3204.

%K nonn

%O 1,1

%A _Reinhard Zumkeller_, Mar 30 2002

%E Terms a(13) and beyond from _Giovanni Resta_, Apr 20 2020