proposed

approved

editing

proposed

Cf. A004611, A106505, A229858, A229859.

proposed

editing

editing

proposed

\\ e.g. pt120b(10080) gives [5, 8, 16, 24, 33, 35, 39, 45, 51, 56, 57, 63, 77, 80, 85, 88, 91, 95]

allocated for Colin BarkerConsider 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

1,1

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.

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

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

(PARI)

\\ Gives values of B not exceeding bmax

\\ e.g. pt120b(100) gives [5, 8, 16, 24, 33, 35, 39, 45, 51, 56, 57, 63, 77, 80, 85, 88, 91, 95]

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)

}

Cf. A004611, A106505.

allocated

nonn

Colin Barker, Oct 06 2013

approved

editing

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

allocated for Colin Barker

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

1,1

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

A229848 gives the values of A, and A004611 gives the values of C.

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

Cf. A004611, A229848.

nonn,changed

allocated

Colin Barker, Oct 01 2013

proposed

approved

editing

proposed

allocated for Colin BarkerConsider 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

1,1

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

A229848 gives the values of A, and A004611 gives the values of C.

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

Cf. A004611, A229848.

allocated

nonn

Colin Barker, Oct 01 2013

approved

editing

allocated for Colin Barker

allocated

approved