A350347 Consider primitive 120-degree integer triangles with sides A < B < C = A002476(n). This sequence gives the values of B.

5, 8, 16, 24, 33, 35, 56, 45, 63, 51, 57, 77, 95, 120, 91, 115, 143, 112, 105, 175, 165, 195, 168, 145, 224, 261, 217, 192, 288, 247, 320, 272, 280, 315, 273, 259, 385, 304, 399, 407, 299, 287, 440, 437, 301, 387, 425, 533, 416, 368, 575, 520, 423, 459, 616, 517, 441, 400, 539, 616, 637, 600, 480, 520, 728, 735, 725

Offset

1,1

Links

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

Wikipedia, Integer triangle

Formula

Let A = A349772(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 b if a * a + a * b + b * b == n * n
    }
  }
end
def A350347(n)
  ary = []
  i = 1
  while ary.size < n
    ary << A(i) if i.prime? && i % 6 == 1
    i += 1
  end
  ary
end
p A350347(100)

Crossrefs

Cf. A002365, A002476 (C), A229849, A264827, A349772 (A).

Sequence in context: A229849 A357276 A088586 * A073136 A063924 A340997

Adjacent sequences: A350344 A350345 A350346 * A350348 A350349 A350350

Keyword

nonn

Author

Seiichi Manyama, Dec 26 2021

Status

approved