A350039 Perimeters of more than one primitive 60-degree integer triangle.

1260, 2520, 2574, 3080, 3740, 3780, 3978, 4620, 4940, 5148, 5720, 5814, 5940, 6435, 6930, 7020, 7280, 7560, 7820, 7866, 7956, 8190, 8550, 8580, 8892, 9044, 10010, 10350, 10395, 10472, 10640, 11628, 11880, 12006, 12240, 12870, 12920, 13050, 13260, 13340, 13680, 13685, 13832, 13860, 13950

Offset

1,1

Links

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

Example

399^2 + 440^2 - 399*440 = 421^2, 56^2 + 615^2 - 56*615 = 589^2 and 399 + 440 + 421 = 56 + 615 + 589 = 1260. So 1260 is a term.
5159^2 + 5904^2 - 5159*5904 = 5569^2, 3344^2 + 7119^2 - 3344*7119 = 6169^2, 1287^2 + 7952^2 - 1287*7952 = 7393^2 and 5159 + 5904 + 5569 = 3344 + 7119 + 6169 = 1287 + 7952 + 7393 = 16632. So 16632 is a term.

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(100).group_by(&:to_i).select{|k, v| v.size > 1}.keys.sort[0..50]

Crossrefs

Cf. A024408, A242039, A350038.

Sequence in context: A291714 A350375 A179690 * A158737 A252277 A203402

Adjacent sequences: A350036 A350037 A350038 * A350040 A350041 A350042

Keyword

nonn

Author

Seiichi Manyama, Dec 10 2021

Status

approved