A164282 Hypotenuses of more than two Pythagorean triangles.

65, 85, 125, 130, 145, 170, 185, 195, 205, 221, 250, 255, 260, 265, 290, 305, 325, 340, 365, 370, 375, 377, 390, 410, 425, 435, 442, 445, 455, 481, 485, 493, 500, 505, 510, 520, 530, 533, 545, 555, 565, 580, 585, 595, 610, 615, 625, 629, 650, 663, 680, 685, 689

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Aug 12 2009

Keywords

• nonn

Comments

Also, hypotenuses c of Pythagorean triangles with legs a and b such that a and b are also the hypotenuses of Pythagorean triangles, where the Pythagorean triples (x1,y1,a) and (x2,y2,b) are similar triangles, but the Pythagorean triples (a,b,c) and (x1,y1,a) are not similar. For example, 65^2 = 25^2 + 60^2 with 25^2 = 15^2 + 20^2 and 60^2 = 36^2 + 48^2 with the two smaller triangles being similar. - Naohiro Nomoto

Examples

			65 is included because there are 4 distinct Pythagorean triangles with hypotenuse 65. In particular, 65^2 = 16^2 + 63^2 = 25^2 + 60^2 = 33^2 + 56^2 = 39^2 + 52^2.
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A009177, A084646, A084647, A084648, A084649.

Programs

Mathematica

Clear[lst,f,n,i,k] f[n_]:=Module[{i=0,k=0},Do[If[Sqrt[n^2-i^2]==IntegerPart[Sqrt[n^2-i^2]],k++ ],{i,n-1,1,-1}];k/2]; lst={};Do[If[f[n]>2,AppendTo[lst,n]],{n,5*5!}];lst

PARI

ok(n)={my(t=0); for(k=1, sqrtint(n^2\2), t += issquare(n^2-k^2)); t>2}
select(ok, [1..1000]) \\ Andrew Howroyd, Aug 17 2018

Extensions

Terms a(45) and beyond from Andrew Howroyd, Aug 17 2018