A350045 Numbers that are the perimeter of a primitive 120-degree integer triangle.

15, 28, 40, 66, 77, 91, 104, 126, 144, 153, 170, 187, 190, 209, 220, 228, 260, 276, 286, 299, 322, 325, 345, 350, 390, 400, 420, 435, 442, 464, 476, 493, 496, 522, 527, 544, 551, 558, 589, 608, 620, 630, 646, 665, 672, 703, 714, 740, 770, 777, 798, 805, 814, 840, 851, 861, 874, 888, 902, 920, 943, 946, 950

Offset

1,1

Links

Seiichi Manyama, Table of n, a(n) for n = 1..10000

Example

b(n) = Sum_{k=1..3} A264827(3*n+k-3).
b(1) = 3+5+7 = 15 = a(1).
b(2) = 5+16+19 = 40 = a(3).
b(3) = 7+8+13 = 28 = a(2).
b(4) = 7+33+37 = 77 = a(5).
b(5) = 9+56+61 = 126 = a(8).
b(6) = 11+24+31 = 66 = a(4).
b(7) = 11+85+91 = 187 = a(12).
b(8) = 13+35+43 = 91 = a(6).

Prog

(Ruby)
def A(n)
  ary = []
  (1..n).each{|i|
    (i + 1..n).each{|j|
      if i.gcd(j) == 1 && (i - j) % 3 > 0
        ary << 2 * j * j + 3 * i * j + i * i
      end
    }
  }
  ary
end
p A(30).uniq.sort[0..100]

Crossrefs

Cf. A002476, A264827, A350038, A350047.

Sequence in context: A045192 A039285 A043888 * A357278 A343067 A223442

Adjacent sequences: A350042 A350043 A350044 * A350046 A350047 A350048

Keyword

nonn

Author

Seiichi Manyama, Dec 11 2021

Status

approved