A068964 Numbers that define integer Heronian triangles [prime(a(n)), prime(a(n)+1), A068965(n)] with area A068966(n).

2, 5, 24, 49, 87, 182, 307, 379, 458, 677, 1618, 2427, 4397, 4944, 5969, 6496, 8871, 9526, 11580, 13063, 16243, 17970, 18400, 20225, 25271, 28275, 37730, 42387, 46597, 48681, 50329, 56586, 58859, 61930, 64289, 65078, 70776, 78360, 80133, 83638, 83640, 115956, 118712

Offset: 1

Author

Reinhard Zumkeller, Mar 30 2002

Keywords

• nonn

Examples

			a(3) = 24: [A000040(24), A000040(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 A068966(3) = 3204.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..385
• Eric Weisstein's World of Mathematics, Heronian Triangle.

Extensions

Terms a(13) and beyond from Giovanni Resta, Apr 20 2020