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

1,1

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.

Links

Table of n, a(n) for n=1..56.

Wikipedia, Integer triangle

Example

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

Prog

(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)
}

Crossrefs

Cf. A004611, A106505, A229858, A229859.

Sequence in context: A001082 A242090 A030006 * A357276 A088586 A350347

Adjacent sequences: A229846 A229847 A229848 * A229850 A229851 A229852

Keyword

nonn

Author

Colin Barker, Oct 06 2013

Status

approved