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A096377 Floor of area of triangle with consecutive prime sides. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 18 05:52 EST 2022. Contains 350428 sequences. (Running on oeis4.)