A103246 Numbers y, without duplication, in Pythagorean triples x,y,z where x,y,z are relatively prime composite numbers.

21, 27, 33, 55, 57, 63, 75, 77, 81, 87, 91, 93, 99, 105, 111, 115, 117, 119, 123, 125, 129, 133, 135, 143, 147, 153, 155, 161, 165, 171, 177, 183, 185, 187, 189, 195, 201, 203, 207, 213, 215, 217, 219, 225, 235, 237, 243, 247, 249, 253, 255, 259, 265, 267, 273

Offset: 1

Author

Cino Hilliard, Mar 19 2005

Keywords

• easy
• nonn

Comments

The example is the smallest such triple in terms of x. In terms of y, 220^2 + 21^2 = 221^2 is the smallest such triple.

Evidently the triples here are ordered so that x is even and y is odd. - Robert Israel, Oct 22 2018

Examples

			x=16, y=63, 16^2 + 63^2 = 65^2. 63 is the 6th entry in the list.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000
• MathForFun, Pythagorean triples
• MathForFun, Pythagorean triples [Cached copy]
• Chenglong Zou, Peter Otzen, Cino Hilliard, Pythagorean triplets, digest of 6 messages in mathfun Yahoo group, Mar 19, 2005.

Programs

Maple

N:= 1000: # to get all terms <= N
Res:= NULL:
for m from 1 to N by 2 do
  for n from 1 to m-2 by 2 while m*n <= N do
    if igcd(m,n) > 1 then next fi;
    if not isprime(m*n) and not isprime((m^2+n^2)/2) then
      Res:= Res, m*n;
    fi
od od:
sort(convert({Res},list)); # Robert Israel, Oct 22 2018

PARI

pythtri(n) = { local(a,b,c=0,k,x,y,z,vy,j); w = 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++; w[c]=y; ) ) ) ); vy=vector(c); w=vecsort(w); for(j=1,n*n, if(w[j]>0, k++; vy[k]=w[j]; ) ); for(j=1,200, if(vy[j+1]<>vy[j],print1(vy[j]",")) ) }