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A127923 Difference between squares of legs of primitive Pythagorean triangles, sorted (with multiplicity). 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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

LINKS

Table of n, a(n) for n=1..41.

CROSSREFS

Cf. A058529, A120681, A120682.

Sequence in context: A007398 A290204 A138629 * A230018 A165563 A034575

Adjacent sequences:  A127920 A127921 A127922 * A127924 A127925 A127926

KEYWORD

nonn

AUTHOR

Lekraj Beedassy, Feb 06 2007

EXTENSIONS

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

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

STATUS

approved

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Last modified July 23 12:49 EDT 2019. Contains 325254 sequences. (Running on oeis4.)