A097442 Integer part of the area of consecutive prime sided isosceles triangles.

2, 7, 16, 36, 64, 102, 144, 198, 306, 397, 520, 676, 774, 898, 1116, 1396, 1575, 1819, 2097, 2264, 2557, 2883, 3267, 3835, 4296, 4533, 4830, 5080, 5394, 6426, 7275, 7881, 8285, 9159, 9784, 10392, 11213, 11879, 12651, 13555, 14080, 15221, 16016, 16573

Offset

2,1

Comments

The real part of these numbers is always irrational.

Links

Harvey P. Dale, Table of n, a(n) for n = 2..1000

Formula

Consider prime isosceles triangles of sides (2, 3, 3), (3, 5, 5), ..., (x, y, y) where x is prime and y is the next prime after x. Then area = 1/2*x*sqrt(y^2-(x/2)^2). Output floor(area)

Mathematica

Floor[#[[1]]/2 Sqrt[#[[2]]^2-(#[[1]]/2)^2]]&/@Partition[Prime[Range[50]], 2, 1] (* Harvey P. Dale, Feb 03 2025 *)

Prog

(PARI) f(n) = forprime(x=2, n, y=nextprime(x+1); a=1/2*x*sqrt(y^2-(x/2)^2); print1(floor (a)", "))

Crossrefs

Sequence in context: A259966 A283500 A394192 * A345025 A329324 A131405

Adjacent sequences: A097439 A097440 A097441 * A097443 A097444 A097445

Keyword

nonn

Author

Cino Hilliard, Aug 22 2004

Status

approved