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 A229849 Consider all primitive 120-degree triangles with sides A < B < C. The sequence gives the values of B. 4
 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 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 A350347 A073136 Adjacent sequences:  A229846 A229847 A229848 * A229850 A229851 A229852 KEYWORD nonn AUTHOR Colin Barker, Oct 06 2013 STATUS approved

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Last modified January 26 07:04 EST 2022. Contains 350572 sequences. (Running on oeis4.)