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.

A331695 Numerator of the x-coordinate of the 3rd point (x,y) of the n-th triangle with integer sides in the list given by A316841, when the triangle is drawn with the longest side from (0,0) to (0,A316843(n)) and the middle side A316844(n) from (0,A316843(n)) to (x,y). x = a(n)/A331696(n), y = sqrt(A331697(n))/A331696(n).

Original entry on oeis.org

1, 1, 1, 3, 1, 2, 3, 11, 2, 1, 1, 9, 2, 5, 13, 9, 5, 1, 2, 9, 8, 5, 29, 3, 5, 5, 9, 3, 1, 1, 3, 4, 25, 3, 7, 33, 20, 7, 17, 11, 29, 19, 7, 1, 2, 9, 8, 25, 18, 7, 55, 4, 37, 11, 53, 4, 19, 3, 31, 5, 51, 4, 1, 1, 9, 1, 25, 9, 49, 4, 9, 61, 35, 9, 41, 8, 19, 34
Offset: 1

Views

Author

Hugo Pfoertner, Jan 25 2020

Keywords

Comments

The shortest side of the triangle has length A316845(n), i.e., x^2 + y^2 = A316845(n)^2.

Examples

			x(n) = a(n)/A331696(n),
y(n) = sqrt(A331697(n))/A331696(n).
   n i (A316843)
   | | j (A316844)
   | | | k (A316845)
   | | | |  a(n) this sequence
   | | | |  |  A331696
   | | | |  |  |   A331697
   | | | |  |  |   |  (x,y)
   1 1 1 1  1  2   3  (0.5000,0.86603)
   2 2 2 1  1  4  15  (0.2500,0.96825)
   3 2 2 2  1  1   3  (1.0000,1.7321)
   4 3 2 2  3  2   7  (1.5000,1.3229)
   5 3 3 1  1  6  35  (0.16667,0.98601)
   6 3 3 2  2  3  32  (0.66667,1.8856)
   7 3 3 3  3  2  27  (1.5000,2.5981)
   8 4 3 2 11  8 135  (1.3750,1.4524)
   9 4 3 3  2  1   5  (2.0000,2.2361)
  10 4 4 1  1  8  63  (0.12500,0.99216)
  11 4 4 2  1  2  15  (0.50000,1.9365)
  12 4 4 3  9  8 495  (1.1250,2.7811)
  13 4 4 4  2  1  12  (2.0000,3.4641)
  14 5 3 3  5  2  11  (2.5000,1.6583)
  15 5 4 2 13 10 231  (1.3000,1.5199)
  16 5 4 3  9  5 144  (1.8000,2.4000)

Crossrefs

Cf. A316841.
Sides of triangle: A316843, A316844, A316845.
Cf. A331696, A331697.

A331696 Common denominator of x-coordinate and y-coordinate of 3rd point of triangles with integer sides corresponding to A331695 and A331697.

Original entry on oeis.org

2, 4, 1, 2, 6, 3, 2, 8, 1, 8, 2, 8, 1, 2, 10, 5, 2, 10, 5, 10, 5, 2, 12, 1, 4, 3, 4, 1, 12, 3, 4, 3, 12, 1, 2, 14, 7, 2, 14, 7, 14, 7, 2, 14, 7, 14, 7, 14, 7, 2, 16, 1, 16, 4, 16, 1, 16, 2, 16, 2, 16, 1, 16, 4, 16, 1, 16, 4, 16, 1, 2, 18, 9, 2, 18, 3, 6, 9, 2
Offset: 1

Views

Author

Hugo Pfoertner, Jan 25 2020

Keywords

Examples

			See A331695.

Crossrefs

Cf. A316841.
Sides of triangle: A316843, A316844, A316845.
Cf. A331695, A331697.

A331247 Numerator of the x-coordinate of the 3rd point (x,y) of the n-th triangle with integer sides i <= j <= k in a list sorted by increasing area, when the triangle is drawn with the shortest side from (0,0) to (0,i) and the middle side from (0,i) to (x,y). x = a(n)/A331248(n), y = sqrt(A331249(n))/A331248(n).

Original entry on oeis.org

1, 1, 1, 1, 1, 9, 1, 1, 11, 1, 1, 13, 1, 3, 1, 25, 8, 1, 15, 1, 1, 29, 1, 17, 3, 1, 1, 3, 19, 1, 11, 49, 1, 2, 1, 3, 21, 10, 1, 37, 25, 1, 9, 1, 23, 55, 1, 3, 41, 1, 11, 1, 25, 2, 1, 61, 5, 81, 27, 15, 27, 1, 1, 3, 4, 1, 29, 5, 67, 1, 1, 49, 2, 89, 1, 11, 31, 3
Offset: 1

Views

Author

Hugo Pfoertner, Jan 23 2020

Keywords

Comments

The side lengths (i,j,k) of the triangles in the list sorted by area are given in A331251, A331252, and A331253.

Examples

			x(n) = a(n) / A331248(n),
y(n) = sqrt(A331249(n)) / A331248(n),
   n i (A331251)
   | | j (A331252)
   | | | k (A331253)
   | | | |    A^2*16
   | | | |    |  a(n) this sequence
   | | | |    |  |  A331248
   | | | |    |  |  |   A331249
   | | | |    |  |  |   |  (x, y)
   1 1 1 1    3  1  2   3  (0.5000, 0.86603)
   2 1 2 2   15  1  2  15  (0.5000, 1.9365)
   3 1 3 3   35  1  2  35  (0.5000, 2.9580)
   4 2 2 2   48  1  1   3  (1.0000, 1.7321)
   5 1 4 4   63  1  2  63  (0.5000, 3.9686)
   6 2 2 3   63  9  4  63  (2.2500, 1.9843)
   7 1 5 5   99  1  2  99  (0.5000, 4.9749)
   8 2 3 3  128  1  1   8  (1.0000, 2.8284)
   9 2 3 4  135 11  4 135  (2.7500, 2.9047)
  10 1 6 6  143  1  2 143  (0.5000, 5.9791)
  11 1 7 7  195  1  2 195  (0.5000, 6.9821)
  12 2 4 5  231 13  4 231  (3.2500, 3.7997)
  13 2 4 4  240  1  1  15  (1.0000, 3.8730)
  14 3 3 3  243  3  2  27  (1.5000, 2.5981)
  ...
  28 3 4 5  576  3  1  16  (3.0000, 4.0000)

Crossrefs

Cf. A331248, A331249, A331251, A331252, A331253, A331695, A331696, A331697.

A331249 Squared numerator of y-coordinate of 3rd point of n-th triangle with integer sides in a sorted list corresponding to A331247. The y-coordinate is given by sqrt(a(n))/A331248(n).

Original entry on oeis.org

3, 15, 35, 3, 63, 63, 99, 8, 135, 143, 195, 231, 15, 27, 255, 275, 80, 323, 351, 24, 399, 455, 483, 495, 55, 35, 575, 16, 663, 675, 75, 735, 48, 12, 783, 91, 855, 224, 899, 935, 975, 63, 63, 1023, 1071, 1071, 1155, 135, 1235, 80, 320, 1295, 1311, 21, 1443, 1463
Offset: 1

Views

Author

Hugo Pfoertner, Jan 23 2020

Keywords

Examples

			a(1) = 3 because the 3rd point of the smallest triangle with integer sides (1,1,1) is at (x,y)=(1/2,sqrt(3)/2), A331247(1)=1, A331248(1)=2.
See A331247 for an extended list.

Crossrefs

Cf. A331247, A331248, A331251, A331252, A331253, A331695, A331696, A331697.
Showing 1-4 of 4 results.

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