A350038 Numbers that are the perimeter of a primitive 60-degree integer triangle.

18, 20, 35, 36, 45, 56, 77, 84, 90, 104, 110, 120, 126, 135, 143, 170, 176, 182, 189, 198, 209, 210, 216, 221, 252, 260, 264, 266, 270, 272, 273, 297, 299, 323, 350, 351, 360, 368, 374, 378, 380, 390, 396, 425, 432, 437, 459, 462, 464, 468, 476, 494, 495, 506, 527, 551, 561, 570, 575, 585, 594, 608, 612

Offset

1,1

Links

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

Example

b(n) = Sum_{k=1..3} A264826(3*n+k-3).
c(n) = Sum_{k=1..3} A201223(3*n+k-3).
b(1) = c(1) = 3+7+8 = 18 = a(1).
b(2) = c(2) = 5+7+8 = 20 = a(2).
b(3) = c(5) = 5+19+21 = 45 = a(5).
b(4) = c(3) = 7+13+15 = 35 = a(3).
b(5) = c(9) = 7+37+40 = 84 = a(8).
b(6) = c(4) = 8+13+15 = 36 = a(4).

Prog

(Ruby)
def A(n)
  ary = []
  (1..n).each{|i|
    (i + 1..n).each{|j|
      if i.gcd(j) == 1 && (i - j) % 3 > 0
        x, y, z = j * j, i * j, i * i
        ary << 2 * x + 5 * y + 2 * z
        ary << 3 * x + 3 * y
      end
    }
  }
  ary
end
p A(20).uniq.sort[0..100]

Crossrefs

Cf. A024364, A201223, A264826, A350013, A350039.

Sequence in context: A186781 A164711 A338195 * A335897 A036170 A064271

Adjacent sequences: A350035 A350036 A350037 * A350039 A350040 A350041

Keyword

nonn

Author

Seiichi Manyama, Dec 10 2021

Status

approved