A350047 Perimeters of more than one primitive 120-degree integer triangle.

2730, 4080, 7590, 9044, 11704, 12180, 13020, 13485, 13920, 14880, 15810, 16100, 18870, 21090, 22755, 23370, 24752, 25172, 26445, 27060, 28380, 29670, 30315, 31020, 32430, 32890, 33810, 34545, 34580, 36660, 37950, 38038, 38220, 38955, 41340, 42476, 44520, 46046, 46110

Offset

1,1

Links

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

Example

897^2 + 560^2 + 897*560 = 1273^2, 168^2 + 1235^2 + 168*1235 = 1327^2 and 897 + 560 + 1273 = 168 + 1235 + 1327 = 2730. So 2730 is a term.
38640^2 + 5291^2 + 38640*5291 = 41539^2, 23088^2 + 22715^2 + 23088*22715 = 39667^2, 10857^2 + 34040^2 + 10857*34040 = 40573^2 and 38640 + 5291 + 41539 = 23088 + 22715 + 39667 = 10857 + 34040 + 40573 = 85470. So 85470 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
        ary << 2 * j * j + 3 * i * j + i * i
      end
    }
  }
  ary
end
p A(200).group_by(&:to_i).select{|k, v| v.size > 1}.keys.sort[0..50]

Crossrefs

Cf. A350039, A350045.

Sequence in context: A231289 A212725 A031608 * A043579 A166780 A068305

Adjacent sequences: A350044 A350045 A350046 * A350048 A350049 A350050

Keyword

nonn

Author

Seiichi Manyama, Dec 11 2021

Status

approved