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

1,1

Links

Giovanni Resta, Table of n, a(n) for n = 1..385

Eric Weisstein's World of Mathematics, Heronian Triangle.

Example

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.

Crossrefs

Sequence in context: A229210 A047147 A111047 * A200402 A010365 A218939

Adjacent sequences: A068961 A068962 A068963 * A068965 A068966 A068967

Keyword

nonn

Author

Reinhard Zumkeller, Mar 30 2002

Extensions

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

Status

approved