login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Table of n, a(n) for n=1..66.

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

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

License Agreements, Terms of Use, Privacy Policy. .

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