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 A229858 Consider all 120-degree triangles with sides A < B < C. The sequence gives the values of A. 4
 3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS A229859 gives the values of B, and A050931 gives the values of C. This sequence contains every integer larger than 8. - Nathaniel Johnston, Oct 06 2013 LINKS Wikipedia, Integer triangle Kival Ngaokrajang, Illustration of initial terms FORMULA a(n) = n+4 for n>4. a(n) = 2*a(n-1)-a(n-2) for n>6. G.f.: -x*(x^5-x^4+x^2+x-3) / (x-1)^2. EXAMPLE 12 appears in the sequence because there exists a 120-degree triangle with sides 12, 20 and 28. PROG (PARI) \\ Gives values of A not exceeding amax. \\ e.g. t120a(20) gives [3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] t120a(amax) = {   v=pt120a(amax);   s=[];   for(i=1, #v,     for(m=1, amax\v[i],       if(v[i]*m<=amax, s=concat(s, v[i]*m))     )   );   vecsort(s, , 8) } \\ Gives values of A not exceeding amax in primitive triangles. \\ e.g. pt120a(20) gives [3, 5, 7, 9, 11, 13, 15, 16, 17, 19] pt120a(amax) = {   s=[];   for(m=1, (amax-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, a=b);         if(a<=amax, s=concat(s, a))       )     )   );   vecsort(s, , 8) } CROSSREFS Cf. A050931, A229849, A229859. Sequence in context: A324060 A323828 A079581 * A269020 A057716 A138591 Adjacent sequences:  A229855 A229856 A229857 * A229859 A229860 A229861 KEYWORD nonn,easy AUTHOR Colin Barker, Oct 06 2013 STATUS approved

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Last modified March 30 22:55 EDT 2020. Contains 333132 sequences. (Running on oeis4.)