A126611 -id:A126611 - cp's OEIS frontend

A126637 Difference x-y of generator pairs (x,y) {x and y coprime and not both odd, x>y} of primitive Pythagorean triangles, sorted on values x+y (A126611), then on x-y.

1, 1, 3, 1, 3, 5, 1, 5, 7, 1, 3, 5, 7, 9, 1, 3, 5, 7, 9, 11, 1, 7, 11, 13, 1, 3, 5, 7, 9, 11, 13, 15, 1, 3, 5, 7, 9, 11, 13, 15, 17, 1, 5, 11, 13, 17, 19, 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 1, 3, 7, 9, 11, 13, 17, 19, 21, 23, 1, 5, 7, 11

Offset: 1

Lekraj Beedassy, Feb 08 2007

This sequence gives the consecutive rows n = 2*m + 1, for m >= 1, of the array A216319. See the example. - Wolfdieter Lang, Oct 24 2019

			From _Wolfdieter Lang_, Oct 24 2019: (Start)
From the array A216319 with n = 2*m + 1 = x + y, for m >= 1, the (x, y) values giving the terms of the present sequence as values x-y are:
m, n \ k    1      2      3      4      5      6 ...   x-y values
--------------------------------------------------------------------
1,  3:   (2,1)                                         1
2,  5:   (3,2) (4,1)                                   1 3
3,  7:   (4,3) (5,2)   (6,1)                           1 3  5
4,  9:   (5,4) (7,2)   (8,1)                           1 5  7
5, 11:   (6,5) (7,4)   (8,3)  (9,2) (10,1)             1 3  5  7  9
6, 13:   (7,6) (8,5)   (9,4) (10,3) (11,2) (12,1)      1 3  5  7  9  11
7, 15:   (8,7) (11,4) (13,2) (14,1)                    1 7 11 13
... (End)

Cf. A094192, A094193, A126611, A216319.

A309424 Sum x+y of generator pairs (x, y) {x and y coprime and not both odd} of primitive Pythagorean triangles, sorted by x and y (for same x).

Original entry on oeis.org

3, 5, 5, 7, 7, 9, 7, 11, 9, 11, 13, 9, 11, 13, 15, 11, 13, 17, 11, 13, 17, 19, 13, 15, 17, 19, 21, 13, 17, 19, 23, 15, 17, 19, 21, 23, 25, 15, 17, 19, 23, 25, 27, 17, 19, 23, 29, 17, 19, 21, 23, 25, 27, 29, 31, 19, 21, 23, 25, 27, 29, 31, 33, 19, 23, 25, 29, 31, 35, 21, 23, 25, 27, 29, 31, 33, 35, 37, 21, 23, 27, 29, 31, 33, 37, 39

Offset: 1

Rui Lin, Jul 31 2019

nonn

This sequence is based on x and y (for same x) in increasing order, directly mapping to A094192 and A094193, while A126611 is sorted by the sum x+y.
Given any 2 of below 4 sequences, primitive Pythagorean triangles can be generated.
A094192: the bigger one in generator pairs;
A094193: the smaller one in generator pairs;
A309424: the sum of generator pairs;
A309425: the difference of generator pairs.

Cf. A094192, A094193, A126611, A309425.

a(n) = A094192(n) + A094193(n).

cp's OEIS Frontend

A126637 Difference x-y of generator pairs (x,y) {x and y coprime and not both odd, x>y} of primitive Pythagorean triangles, sorted on values x+y (A126611), then on x-y.

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