A098714 - OEIS

%I #30 Feb 07 2020 14:07:29

%S 12,24,30,36,40,48,56,70,72,80,96,108,112,126,140,150,154,156,160,176,

%T 182,192,198,200,204,208,216,220,224,228,234,260,276,286,306,308,320,

%U 324,340,348,350,352,364,372,374,378,380,384,392,400,416,418,442,444

%N Only one Pythagorean triangle of this perimeter exists.

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

%C Numbers in A010814 not in A009129. - _Hugo Pfoertner_, Mar 29 2018

%H Ray Chandler, <a href="/A098714/b098714.txt">Table of n, a(n) for n = 1..10000</a> (first 5000 terms from Hugo Pfoertner)

%H Project Euler, <a href="https://projecteuler.net/problem=75">Problem 75: Singular integer right triangles</a>.

%H <a href="/index/Ps#PyTrip">Index entries related to Pythagorean triples.</a>

%F 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.

%o (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

%Y Cf. A009129, A010814.

%K nonn

%O 1,1

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

%E More terms from _Hugo Pfoertner_ and _Ray Chandler_, Oct 27 2004

%E New name from _Hugo Pfoertner_, Mar 29 2018