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

Author

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

Keywords

• nonn

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.

Crossrefs

Cf. A009129, A010814.

Programs

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

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.

Extensions

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

New name from Hugo Pfoertner, Mar 29 2018