A127923 Difference between squares of legs of primitive Pythagorean triangles, sorted (with multiplicity).

7, 41, 119, 161, 239, 527, 721, 959, 1081, 1241, 1393, 1519, 2047, 3281, 3479, 3713, 4207, 4633, 4681, 4879, 5593, 6647, 6887, 7327, 8119, 9401, 9641, 10199, 11753, 12121, 12319, 12593, 16999, 19159, 19199, 19873, 20447, 22393, 23359, 24521, 24521

Offset: 1

Author

Lekraj Beedassy, Feb 06 2007

Keywords

• nonn

Comments

This is the sorted sequence of all products A120681(i)*A120682(i). - R. J. Mathar, Sep 24 2007

The sequence is conjectural (and may miss entries) because it is generated from a finite list of primitive Pythagorean triangles. The associated lengths in a^2+b^2=c^2 are (a,b)=(3,4), (21,20), (5,12), (15,8), (119,120), (7,24), (55,48), (65,72), (35,12), (45,28), (697,696), (9,40), (33,56), (105,88), (11,60), (63,16), (297,304), (77,36), (91,60), (39,80), (403,396), (133,156), (13,84), (207,224), (4059, 4060), (99,20), (171,140), (85,132), (117,44), (275,252), (15,112), (153,104), (51,140), (555,572), (95,168), (143,24), (17,144), (253, 204), (225,272), (165,52), (1755,1748), (429,460),... with gcd(a, b)=1 and |a^2-b^2| in the sequence. - R. J. Mathar, Sep 24 2007

Confirmed sequence is accurate and complete. Observe that both b-a and b+a must be in A058529. Running through the possible combinations of those values with products below 25000 that produce values of a and b that are legs of primitive Pythagorean triangles confirms list is correct. Note that terms of this sequence must also be in A058529. - Ray Chandler, Apr 11 2010

24521 appears twice in the sequence for (a,b)=(52,165) and (1748,1755). - Ray Chandler, Apr 11 2010

Crossrefs

Cf. A058529, A120681, A120682.

Extensions

More terms from R. J. Mathar, Sep 24 2007

Removed "conjectural" from description by Ray Chandler, Apr 11 2010