

A020883


Ordered long legs of primitive Pythagorean triangles.


52



4, 12, 15, 21, 24, 35, 40, 45, 55, 56, 60, 63, 72, 77, 80, 84, 91, 99, 105, 112, 117, 120, 132, 140, 143, 144, 153, 156, 165, 168, 171, 176, 180, 187, 195, 208, 209, 220, 221, 224, 231, 240, 247, 252, 253, 255, 260, 264, 272, 273, 275, 285, 288, 299, 304, 308, 312, 323
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OFFSET

1,1


COMMENTS

Consider primitive Pythagorean triangles (A^2 + B^2 = C^2, (A, B) = 1, A < B); sequence gives values of B, sorted.
Any term in this sequence is given by f(m,n) = 2*m*n or g(m,n) = m^2  n^2 where m and n are any two positive integers, m > 1, n < m, the greatest common divisor of m and n is 1, m and n are not both odd; e.g., f(m,n) = f(2,1) = 2*2*1 = 4.  Agola Kisira Odero, Apr 29 2016
Also, ordered sides a of primitive triples (a, b, c) for integersided triangles where side a is the harmonic mean of the 2 other sides b and c, i.e., 2/a = 1/b + 1/c with b < a < c.
Example: a(2) = 12, because the second triple is (12, 10, 15) with side a = 12, satisfying 2/12 = 1/10 + 1/15 and 1512 < 10 < 15+12.
The first term appearing twice 420 corresponds to triples (420, 310, 651) and (420, 406, 435), the second one is 572 = a(101) = a(102) = A024410(2) and corresponds to triples (572, 407, 962) and (572, 455, 770). The terms that appear more than once in this sequence are in A024410.
For the corresponding primitive triples and miscellaneous properties and references, see A343891. (End)


REFERENCES

V. Lespinard & R. Pernet, Trigonométrie, Classe de Mathématiques élémentaires, programme 1962, problème B337 p. 179, André Desvigne.


LINKS



MAPLE

for a from 4 to 325 do
for b from floor(a/2)+1 to a1 do
c := a*b/(2*ba);
if c=floor(c) and igcd(a, b, c)=1 and cb<a then print(a); end if;
end do;


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



