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 A229839 Consider all 60-degree triangles with sides A < B < C. The sequence gives the values of C. 4
 8, 15, 16, 21, 24, 30, 32, 35, 40, 42, 45, 48, 55, 56, 60, 63, 64, 65, 70, 72, 75, 77, 80, 84, 88, 90, 91, 96, 99, 104, 105, 110, 112, 117, 119, 120, 126, 128, 130, 133, 135, 136, 140, 143, 144, 147, 150, 152, 153, 154, 160, 165, 168, 171, 175, 176, 180, 182 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS A009005 gives the values of A, and A050931 gives the values of B. The side n of an equilateral triangle for which a nontrivial integral cevian of length less than n exists, which divides an edge into two integral parts. - Colin Barker, Sep 09 2014 LINKS Wikipedia, Integer triangle Wikipedia, Cevian EXAMPLE 16 appears in the sequence because there exists a 60-degree triangle with sides 6, 14 and 16. MATHEMATICA list={}; cmax=182; Do[If[IntegerQ[Sqrt[e^2-e t+t^2]], AppendTo[list, e]], {e, 2, cmax}, {t, 1, e-1}] list//DeleteDuplicates (* Herbert Kociemba, Apr 25 2021 *) PROG (PARI) \\ Gives values of C not exceeding cmax. \\ e.g. t60c(60) gives [8, 15, 16, 21, 24, 30, 32, 35, 40, 42, 45, 48, 55, 56, 60] t60c(cmax) = {   v=pt60c(cmax);   s=[];   for(i=1, #v,     for(m=1, cmax\v[i],       if(v[i]*m<=cmax, s=concat(s, v[i]*m))     )   );   vecsort(s, , 8) } \\ Gives values of C not exceeding cmax in primitive triangles. \\ e.g. pt60c(115) gives [8, 15, 21, 35, 40, 48, 55, 65, 77, 80, 91, 96, 99, 112] pt60c(cmax) = {   s=[];   for(m=1, ceil(sqrt(cmax+1)),    for(n=1, m-1,       if((m-n)%3!=0 && gcd(m, n)==1,         if(2*m*n+m*m<=cmax, s=concat(s, 2*m*n+m*m))       )     )   );   vecsort(s, , 8) } CROSSREFS Cf. A009005, A050931, A229838. Cf. A246918, A246919, A246920. Sequence in context: A248389 A301618 A192915 * A114605 A300860 A031103 Adjacent sequences:  A229836 A229837 A229838 * A229840 A229841 A229842 KEYWORD nonn AUTHOR Colin Barker, Oct 01 2013 STATUS approved

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Last modified December 6 15:18 EST 2021. Contains 349563 sequences. (Running on oeis4.)