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

1,1

Links

Seiichi Manyama, Table of n, a(n) for n = 1..1000

Wikipedia, Integer triangle

Formula

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

Example

  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)

Prog

(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)

Crossrefs

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

Sequence in context: A358793 A094009 A328185 * A088514 A357275 A254929

Adjacent sequences: A349769 A349770 A349771 * A349773 A349774 A349775

Keyword

nonn

Author

Seiichi Manyama, Dec 26 2021

Status

approved