A229859 Consider all 120-degree triangles with sides A < B < C. The sequence gives the values of B.

5, 8, 10, 15, 16, 20, 24, 25, 30, 32, 33, 35, 39, 40, 45, 48, 50, 51, 55, 56, 57, 60, 63, 64, 65, 66, 70, 72, 75, 77, 78, 80, 85, 88, 90, 91, 95, 96, 99, 100, 102, 104, 105, 110, 112, 114, 115, 117, 120, 125, 126, 128, 130, 132, 135, 136, 140, 143, 144, 145

Offset: 1

Author

Colin Barker, Oct 06 2013

Keywords

• nonn

Comments

A229858 gives the values of A, and A050931 gives the values of C.

Examples

			20 appears in the sequence because there exists a 120-degree triangle with sides 12, 20 and 28.
		

Links

• Wikipedia, Integer triangle

Crossrefs

Cf. A050931, A229849, A229858.

Programs

PARI

\\ Gives values of B not exceeding bmax.
\\ e.g. t120b(40) gives [5, 8, 10, 15, 16, 20, 24, 25, 30, 32, 33, 35, 39, 40]
t120b(bmax) = {
  v=pt120b(bmax);
  s=[];
  for(i=1, #v,
    for(m=1, bmax\v[i],
      if(v[i]*m<=bmax, s=concat(s, v[i]*m))
    )
  );
  vecsort(s,,8)
}
\\ Gives values of B not exceeding bmax in primitive triangles.
\\ e.g. pt120b(40) gives [5, 8, 16, 24, 33, 35, 39]
pt120b(bmax) = {
  s=[];
  for(m=1, (bmax-1)\2,
    for(n=1, m-1,
      if((m-n)%3!=0 && gcd(m, n)==1,
        a=m*m-n*n;
        b=n*(2*m+n);
        if(a>b, b=a);
        if(b<=bmax, s=concat(s, b))
      )
    )
  );
  vecsort(s,,8)
}