The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 Table of n, a(n) for n=1..58. 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 A352989 Adjacent sequences: A229836 A229837 A229838 * A229840 A229841 A229842 KEYWORD nonn AUTHOR Colin Barker, Oct 01 2013 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 27 11:20 EDT 2024. Contains 372858 sequences. (Running on oeis4.)