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

1,1

Comments

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

Links

Table of n, a(n) for n=1..60.

Wikipedia, Integer triangle

Example

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

Prog

(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)
}

Crossrefs

Cf. A050931, A229849, A229858.

Sequence in context: A314382 A022799 A314383 * A329237 A314384 A196384

Adjacent sequences: A229856 A229857 A229858 * A229860 A229861 A229862

Keyword

nonn

Author

Colin Barker, Oct 06 2013

Status

approved