A249750 Number of primitive Pythagorean triples with perimeter < 10^n.

0, 7, 70, 703, 7026, 70229, 702309, 7023027, 70230484, 702304875, 7023049293, 70230492763, 702304928492, 7023049277919, 70230492773355, 702304927727064, 7023049277265686, 70230492772676557

Offset: 1

Author

Frank M Jackson, Nov 04 2014

Keywords

• nonn
• more

Comments

The ratio a(n)/10^n as n->inf is log(2)/Pi^2 = 0.70230... (Lehmer - A118858).

Examples

			a(2)=7 because there are 7 primitive solutions (a,b,c) with a+b+c<10^2.
(3,4,5),(5,12,13),(8,15,17),(7,24,25),(20,21,29),(12,35,37),(9,40,41)
		

Links

• D. N. Lehmer, Asymptotic evaluation of certain totient sums, Amer. J. Math. 22, 293-335, 1900.
• Eric Weisstein's World of Mathematics, Primitive Pythagorean Triple

Crossrefs

Cf. A118858.

Programs

Mathematica

lst1 = {}; Do[If[GCD[m, n]==1&&m
				

Extensions

a(8)-a(18) from Hiroaki Yamanouchi, Nov 17 2014