A098714 Only one Pythagorean triangle of this perimeter exists.

12, 24, 30, 36, 40, 48, 56, 70, 72, 80, 96, 108, 112, 126, 140, 150, 154, 156, 160, 176, 182, 192, 198, 200, 204, 208, 216, 220, 224, 228, 234, 260, 276, 286, 306, 308, 320, 324, 340, 348, 350, 352, 364, 372, 374, 378, 380, 384, 392, 400, 416, 418, 442, 444

Offset

1,1

Comments

Previous name was : This is the perimeter (n) of square triangles with integer sides and that have only a single solution.

Numbers in A010814 not in A009129. - Hugo Pfoertner, Mar 29 2018

Links

Ray Chandler, Table of n, a(n) for n = 1..10000 (first 5000 terms from Hugo Pfoertner)

Project Euler, Problem 75: Singular integer right triangles.

Index entries related to Pythagorean triples.

Formula

n = a + b + c; c^2=a^2+b^2; a, b, c (sides) and n (perimeter) are integers; for a given "n" there is only a single triple of a, b and c.

Prog

(PARI) forstep(p=12, 444, 2, d=0; for(k=1, p-3, for(j=k+1, p-k-1, if(j*j+k*k==(p-j-k)^2, d++))); if(d==1, print1(p, ", "))) \\ Hugo Pfoertner, Mar 29 2018

Crossrefs

Cf. A009129, A010814.

Sequence in context: A009096 A010814 A334760 * A334758 A299729 A325777

Adjacent sequences: A098711 A098712 A098713 * A098715 A098716 A098717

Keyword

nonn

Author

Marcus Rezende (marcus(AT)anp.gov.br), Sep 29 2004

Extensions

More terms from Hugo Pfoertner and Ray Chandler, Oct 27 2004

New name from Hugo Pfoertner, Mar 29 2018

Status

approved