A103248 Numbers x, without duplication, in Pythagorean triples x,y,z where x,y,z are relatively prime composite numbers.

16, 24, 36, 44, 56, 60, 64, 68, 76, 84, 88, 92, 96, 100, 104, 116, 120, 124, 128, 132, 136, 140, 144, 152, 156, 160, 164, 168, 172, 176, 184, 192, 196, 200, 204, 208, 212, 216, 220, 224, 228, 236, 240, 244, 252, 256, 264, 272, 276, 280, 284, 288, 296, 300, 304

Offset: 1

Author

Cino Hilliard, Mar 19 2005

Keywords

• easy
• nonn

Examples

			x=16, y=63, 16^2 + 63^2 = 65^2. 16 is the 1st entry in the list.
		

Links

• MathForFun, Pythagorean triples
• Chenglong Zou, Peter Otzen, Cino Hilliard, Pythagorean triplets, digest of 6 messages in mathfun Yahoo group, Mar 19, 2005.

Programs

PARI

pythtri(n) = { local(a,b,c=0,k,x,y,z,vx,vy,wx,wyj); wx=wy= vector(n*n); for(a=1,n, for(b=1,n, x=2*a*b; y=b^2-a^2; z=b^2+a^2; if(y > 0 &!isprime(x) &!isprime(y) &!isprime(z), if(gcd(x,y)==1&gcd(x,z)==1&gcd(y,z)==1, c++; wy[c]=y; wx[c]=x; print(x","y","z); \ write("pythtri.txt",x","y","z); ) ) ) ); vy=vx=vector(c); wy=vecsort(wy); wx=vecsort(wx); for(j=1,n*n, if(wx[j]>0, k++; vx[k]=wx[j]; ); ); for(j=1,200, if(vx[j+1]<>vx[j],print1(vx[j]",")) ) }