cp's OEIS Frontend

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

%I A127923 #13 Jul 05 2017 02:56:24
%S A127923 7,41,119,161,239,527,721,959,1081,1241,1393,1519,2047,3281,3479,3713,
%T A127923 4207,4633,4681,4879,5593,6647,6887,7327,8119,9401,9641,10199,11753,
%U A127923 12121,12319,12593,16999,19159,19199,19873,20447,22393,23359,24521,24521
%N A127923 Difference between squares of legs of primitive Pythagorean triangles, sorted (with multiplicity).
%C A127923 This is the sorted sequence of all products A120681(i)*A120682(i). - _R. J. Mathar_, Sep 24 2007
%C A127923 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
%C A127923 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
%C A127923 24521 appears twice in the sequence for (a,b)=(52,165) and (1748,1755). - _Ray Chandler_, Apr 11 2010
%Y A127923 Cf. A058529, A120681, A120682.
%K A127923 nonn
%O A127923 1,1
%A A127923 _Lekraj Beedassy_, Feb 06 2007
%E A127923 More terms from _R. J. Mathar_, Sep 24 2007
%E A127923 Removed "conjectural" from description by _Ray Chandler_, Apr 11 2010