A096377 Floor of area of triangle with consecutive prime sides.

0, 6, 12, 38, 71, 107, 158, 218, 317, 436, 550, 696, 817, 961, 1184, 1425, 1666, 1883, 2134, 2377, 2635, 3008, 3437, 3931, 4351, 4645, 4887, 5199, 5778, 6548, 7484, 7955, 8653, 9237, 10032, 10642, 11389, 12150, 12928, 13653, 14570, 15323, 16232, 16683

Offset

1,2

Links

Table of n, a(n) for n=1..44.

Formula

Given a triangle ABC with sides a, b, base c, height h and x=base of right triangle formed by a and h. Then a^2 = h^2+x^2, b^2 = h^2+(c-x)^2, h = sqrt(a^2 - x^2), area = 1/2hc. Hence x = ( a^2-b^2 + c^2)/2c and so area = 1/4*sqrt(4*a^2*c^2-(a^2-b^2+c^2)^2).

Example

For triangle with sides 3,5,7 area = (1/4)*sqrt(4*9*49 - (9-25+49)^2) = 6.495...

Prog

(PARI) area(n) = { for(x=1, n, a=prime(x); b=prime(x+1); c=prime(x+2); z=1/4*sqrt(4*a^2*c^2-(c^2+a^2-b^2)^2); print1(floor(z)", ") ) }

Crossrefs

Sequence in context: A256875 A117596 A276601 * A026083 A215179 A128453

Adjacent sequences: A096374 A096375 A096376 * A096378 A096379 A096380

Keyword

nonn

Author

Cino Hilliard, Aug 04 2004

Status

approved