A349772 Consider primitive 120-degree integer triangles with sides A < B < C = A002476(n). This sequence gives the values of A.

3, 7, 5, 11, 7, 13, 9, 32, 17, 40, 55, 40, 24, 13, 69, 56, 25, 75, 104, 32, 56, 29, 85, 119, 31, 19, 95, 133, 35, 105, 21, 105, 111, 88, 152, 176, 23, 161, 41, 48, 205, 240, 43, 88, 275, 208, 184, 27, 235, 297, 49, 147, 280, 245, 29, 203, 319, 377, 240, 159, 155, 217, 371, 341, 55, 64, 112

Offset: 1

Author

Seiichi Manyama, Dec 26 2021

Keywords

• nonn

Examples

			  n | ( A,  B,  C)
----+-------------
  1 | ( 3,  5,  7)
  2 | ( 7,  8, 13)
  3 | ( 5, 16, 19)
  4 | (11, 24, 31)
  5 | ( 7, 33, 37)
  6 | (13, 35, 43)
  7 | ( 9, 56, 61)
  8 | (32, 45, 67)
  9 | (17, 63, 73)
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..1000
• Wikipedia, Integer triangle

Crossrefs

Cf. A002366, A002476 (C), A229858, A264827, A350347 (B).

Programs

Ruby

require 'prime'
def A(n)
  (1..n).each{|a|
    (a + 1..n).each{|b|
      return a if a * a + a * b + b * b == n * n
    }
  }
end
def A349772(n)
  ary = []
  i = 1
  while ary.size < n
    ary << A(i) if i.prime? && i % 6 == 1
    i += 1
  end
  ary
end
p A349772(100)

Formula

Let B = A350347(n). A^2 + A*B + B^2 = C^2.