A239581 Number of primitive Pythagorean triangles (x, y, z) with legs x < y < 10^n.

1, 18, 179, 1788, 17861, 178600, 1786011, 17860355, 178603639, 1786036410, 17860362941

Offset: 1

Author

Martin Renner, Mar 26 2014

Keywords

• nonn
• more

Comments

A Pythagorean triangle is a right triangle with integer side lengths x, y, z forming a Pythagorean triple (x, y, z). It is called primitive, if gcd(x, y, z) = 1.

Because (x, y, z) is equivalent to (y, x, z), the total number of primitive Pythagorean triangles with legs x, y < 10^n is b(n) = 2*a(n) = 2, 36, 358, 3576, 35722, ...

Examples

			a(1) = 1, because the only primitive Pythagorean triangle with x < y < 10 is [3, 4, 5].
		

Links

• Eric Weisstein's World of Mathematics, Pythagorean Triangle.
• Eric Weisstein's World of Mathematics, Pythagorean Triple.

Crossrefs

Cf. A008846, A020882, A020883, A020884, A046086, A046087, A101931, A101929, A239744, A239786.

Extensions

a(6)-a(11) from Giovanni Resta, Mar 27 2014