

A020884


Ordered short legs of primitive Pythagorean triangles.


42



3, 5, 7, 8, 9, 11, 12, 13, 15, 16, 17, 19, 20, 20, 21, 23, 24, 25, 27, 28, 28, 29, 31, 32, 33, 33, 35, 36, 36, 37, 39, 39, 40, 41, 43, 44, 44, 45, 47, 48, 48, 49, 51, 51, 52, 52, 53, 55, 56, 57, 57, 59, 60, 60, 60, 61, 63, 64, 65, 65, 67, 68, 68, 69, 69, 71, 72, 73, 75, 75, 76, 76, 77
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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 A, sorted.
Each term in this sequence is given by f(m,n) = m^2  n^2 or g(m,n) = 2mn where m and n are relatively prime positive integers with m > n, m and n not both odd. For example, a(1) = f(2,1) = 2^2  1^2 = 3 and a(4) = g(4,1) = 2*4*1 = 8.  Agola Kisira Odero, Apr 29 2016
All powers of 2 greater than 4 (2^2) are terms, and are generated by the function g(m,n) = 2mn.  Torlach Rush, Nov 08 2019


LINKS

Nick Exner, Generating Pythagorean Triples. This was originally a Java applet (1998), modified by Michael McKelvey in 2001 and redone as an HTML page with JavaScript by Evan Ramos in 2014.


MATHEMATICA

shortLegs = {}; amx = 99; Do[For[b = a + 1, b < (a^2/2), c = (a^2 + b^2)^(1/2); If[c == IntegerPart[c] && GCD[a, b, c] == 1, AppendTo[shortLegs, a]]; b = b + 2], {a, 3, amx}]; shortLegs (* Vladimir Joseph Stephan Orlovsky, Aug 07 2008 *)


PROG

(Haskell)
a020884 n = a020884_list !! (n1)
a020884_list = f 1 1 where
f u v  v > uu `div` 2 = f (u + 1) (u + 2)
 gcd u v > 1  w == 0 = f u (v + 2)
 otherwise = u : f u (v + 2)
where uu = u ^ 2; w = a037213 (uu + v ^ 2)


CROSSREFS

Cf. A024359 (gives the number of times n occurs).


KEYWORD

nonn,easy,nice


AUTHOR



EXTENSIONS



STATUS

approved



