A014498 - OEIS

%I #20 Oct 27 2023 22:00:43

%S 1,2,3,3,6,5,4,10,5,12,7,15,14,6,15,20,9,21,7,18,28,11,8,21,30,35,22,

%T 9,36,24,35,13,42,33,45,10,26,40,44,15,39,11,30,45,55,56,30,63,52,12,

%U 33,66,17,63,65,72,34,13,77,60,55,70,78,19,51,14,88,39,60,77,38,91,68,90

%N Varying radii of inscribed circles within primitive Pythagorean triples as a function of increasing values of hypotenuse.

%H Ray Chandler, <a href="/A014498/b014498.txt">Table of n, a(n) for n = 1..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PythagoreanTriple.html">Pythagorean Triple.</a>

%H Saltire Software, <a href="http://www.saltire.com/HTML5/Basic Geometry/Pythagorean Triples.html">Pythagorean Triples</a>

%F Arrange all primitive Pythagorean triples a, b, c by value of hypotenuse c, then by long leg b; for n-th value of c, sequence gives radius of largest inscribed circle, (a+b-c)/2.

%F a(n) = (A046086(n) + A046087(n) - A020882(n))/2 = A087459(n)/2.

%F a(n) = sqrt{(A118961(n)*A118962(n)/2}. - _Lekraj Beedassy_, May 07 2006

%Y For ordered values of (a+b-c)/2 see A020888.

%Y Cf. A046086, A046087, A020882, A087459.

%K nonn

%O 1,2

%A RALPH PETERSON (ralphp(AT)LIBRARY.NRL.NAVY.MIL)

%E More terms from _Asher Auel_ May 05 2000

%E Extended by _Ray Chandler_, Mar 09 2004