cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A264826 Primitive Eisenstein triples: (a,b,c) in lexicographic order such that a^2 + b^2 - a*b - c^2 = 0, a < b < c, and gcd(a, b) = 1.

Original entry on oeis.org

3, 7, 8, 5, 7, 8, 5, 19, 21, 7, 13, 15, 7, 37, 40, 8, 13, 15, 9, 61, 65, 11, 31, 35, 11, 91, 96, 13, 43, 48, 13, 127, 133, 15, 169, 176, 16, 19, 21, 16, 49, 55, 17, 73, 80, 17, 217, 225, 19, 91, 99, 19, 271, 280, 21, 331, 341, 23, 133, 143, 23, 397, 408
Offset: 1

Views

Author

Colin Barker, Nov 26 2015

Keywords

Comments

The sides of a primitive 60-degree integer triangle.

Links

Crossrefs

Cf. A089025, A121992, A201223, A263728, A264827.

Programs

  • PARI
    pt60(a) = {
  my(L=List(), n=-3*a^2, f, g, b, c);
  fordiv(n, f,
    g=n\f;
    if(f>g && (g+f)%2==0 && (f-g)%4==0,
      b=(f-g)\4; c=((f+g)\2+a)\2;
      if(c>0 && a

A350045 Numbers that are the perimeter of a primitive 120-degree integer triangle.

Original entry on oeis.org

15, 28, 40, 66, 77, 91, 104, 126, 144, 153, 170, 187, 190, 209, 220, 228, 260, 276, 286, 299, 322, 325, 345, 350, 390, 400, 420, 435, 442, 464, 476, 493, 496, 522, 527, 544, 551, 558, 589, 608, 620, 630, 646, 665, 672, 703, 714, 740, 770, 777, 798, 805, 814, 840, 851, 861, 874, 888, 902, 920, 943, 946, 950
Offset: 1

Views

Author

Seiichi Manyama, Dec 11 2021

Keywords

Examples

			b(n) = Sum_{k=1..3} A264827(3*n+k-3).
b(1) = 3+5+7 = 15 = a(1).
b(2) = 5+16+19 = 40 = a(3).
b(3) = 7+8+13 = 28 = a(2).
b(4) = 7+33+37 = 77 = a(5).
b(5) = 9+56+61 = 126 = a(8).
b(6) = 11+24+31 = 66 = a(4).
b(7) = 11+85+91 = 187 = a(12).
b(8) = 13+35+43 = 91 = a(6).

Links

Crossrefs

Cf. A002476, A264827, A350038, A350047.

Programs

  • 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(30).uniq.sort[0..100]

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

Original entry on oeis.org

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

Views

Author

Seiichi Manyama, Dec 26 2021

Keywords

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

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.

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

Original entry on oeis.org

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

Views

Author

Seiichi Manyama, Dec 26 2021

Keywords

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

Crossrefs

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

Programs

  • 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)

Formula

Let A = A349772(n). A^2 + A*B + B^2 = C^2.
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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