

A020884


Ordered short legs of primitive Pythagorean triangles.


38



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.
Union of A081874 and A081925.  Lekraj Beedassy, Jul 28 2006
Any term in this sequence is given by f(m,n) = m^2  n^2 where m and n are any two 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(2,1) = 2^2  1^2 = 3.  Agola Kisira Odero, Apr 29 2016


LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000
P. Alfeld, Pythagorean Triples (broken link)
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.
W. A. Kehowski, Pythagorean Triples (broken link)
Ron Knott, Pythagorean Triples and Online Calculators


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)
 Reinhard Zumkeller, Nov 09 2012


CROSSREFS

Cf. A009004, A020882A020886. Different from A024352.
Cf. A024359 (gives the number of times n occurs).
Cf. A037213.
Sequence in context: A025050 A196115 A025051 * A183855 A024352 A288525
Adjacent sequences: A020881 A020882 A020883 * A020885 A020886 A020887


KEYWORD

nonn,easy,nice


AUTHOR

Clark Kimberling


EXTENSIONS

Extended and corrected by David W. Wilson


STATUS

approved



