A229849 - OEIS

%I #10 Oct 06 2013 15:29:00

%S 5,8,16,24,33,35,39,45,51,56,57,63,77,80,85,88,91,95,105,112,115,120,

%T 143,145,155,160,161,165,168,175,187,192,195,203,208,209,217,221,224,

%U 231,247,253,259,261,272,273,279,280,287,288,299,301,304,315,320,323

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

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

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

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Integer_triangle">Integer triangle</a>

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

%o (PARI)

%o \\ Gives values of B not exceeding bmax

%o \\ e.g. pt120b(80) gives [5, 8, 16, 24, 33, 35, 39, 45, 51, 56, 57, 63, 77, 80]

%o pt120b(bmax) = {

%o   s=[];

%o   for(m=1, (bmax-1)\2,

%o     for(n=1, m-1,

%o       if((m-n)%3!=0 && gcd(m, n)==1,

%o         a=m*m-n*n;

%o         b=n*(2*m+n);

%o         if(a>b, b=a);

%o         if(b<=bmax, s=concat(s, b))

%o       )

%o     )

%o   );

%o   vecsort(s,,8)

%o }

%Y Cf. A004611, A106505, A229858, A229859.

%K nonn

%O 1,1

%A _Colin Barker_, Oct 06 2013