A239581 - OEIS

%I #33 Mar 03 2023 14:08:43

%S 1,18,179,1788,17861,178600,1786011,17860355,178603639,1786036410,

%T 17860362941

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

%C 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.

%C 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, ...

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PythagoreanTriangle.html">Pythagorean Triangle</a>.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PythagoreanTriple.html">Pythagorean Triple</a>.

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

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

%K nonn,more

%O 1,2

%A _Martin Renner_, Mar 26 2014

%E a(6)-a(11) from _Giovanni Resta_, Mar 27 2014