A229849 Consider all primitive 120-degree triangles with sides A < B < C. The sequence gives the values of B.

5, 8, 16, 24, 33, 35, 39, 45, 51, 56, 57, 63, 77, 80, 85, 88, 91, 95, 105, 112, 115, 120, 143, 145, 155, 160, 161, 165, 168, 175, 187, 192, 195, 203, 208, 209, 217, 221, 224, 231, 247, 253, 259, 261, 272, 273, 279, 280, 287, 288, 299, 301, 304, 315, 320, 323

Offset: 1

Author

Colin Barker, Oct 06 2013

Keywords

• nonn

Comments

A primitive triangle is one for which the sides have no common factor.

For n>1, A106505(n) seems to give the values of A and A004611(n) seems to give the values of C.

Examples

			33 appears in the sequence because there exists a primitive 120-degree triangle with sides 7, 33 and 37.
		

Links

• Wikipedia, Integer triangle

Crossrefs

Cf. A004611, A106505, A229858, A229859.

Programs

PARI

\\ Gives values of B not exceeding bmax
\\ e.g. pt120b(80) gives [5, 8, 16, 24, 33, 35, 39, 45, 51, 56, 57, 63, 77, 80]
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)
}