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A229849 Consider all primitive 120-degree triangles with sides A < B < C. The sequence gives the values of B. 3
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 (list; graph; refs; listen; history; text; internal format)
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 * A088586 A073136 A063924

Adjacent sequences:  A229846 A229847 A229848 * A229850 A229851 A229852

KEYWORD

nonn

AUTHOR

Colin Barker, Oct 06 2013

STATUS

approved

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Last modified April 3 19:43 EDT 2020. Contains 333198 sequences. (Running on oeis4.)