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Areas of integer Heronian triangles [prime(A068964(n)), prime(A068964(n)+1), A068965(n)].
4

%I #14 Apr 20 2020 05:35:47

%S 6,66,3204,6810,37716,72006,182430,532236,370614,2155134,3203694,

%T 6353634,51712890,42020844,28698786,33163770,55637466,125033580,

%U 172985436,105470250,151375626,178631034,185921166,217064574,939603126,376267326,1812742734,2193232470,853918566

%N Areas of integer Heronian triangles [prime(A068964(n)), prime(A068964(n)+1), A068965(n)].

%H Giovanni Resta, <a href="/A068966/b068966.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>.

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

%e A068964(3) = 24: [prime(24), prime(25), A068965(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 a(3) = 3204.

%Y Cf. A046131, A055595, A068969.

%K nonn

%O 1,1

%A _Reinhard Zumkeller_, Mar 30 2002

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