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

1,1

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

Links

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

Example

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.

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

Prog

(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

Crossrefs

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

Sequence in context: A214484 A159758 A056693 * A025312 A024508 A025303

Adjacent sequences: A164279 A164280 A164281 * A164283 A164284 A164285

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Aug 12 2009

Extensions

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

Status

approved