

A014498


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


9



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, 9, 36, 24, 35, 13, 42, 33, 45, 10, 26, 40, 44, 15, 39, 11, 30, 45, 55, 56, 30, 63, 52, 12, 33, 66, 17, 63, 65, 72, 34, 13, 77, 60, 55, 70, 78, 19, 51, 14, 88, 39, 60, 77, 38, 91, 68, 90
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OFFSET

1,2


LINKS

Table of n, a(n) for n=1..74.
Eric Weisstein's World of Mathematics, Pythagorean Triple.
Saltire Software, Pythagorean Triples


FORMULA

Arrange all primitive Pythagorean triples a, b, c by value of hypotenuse c, then by long leg b; for nth value of c, sequence gives radius of largest inscribed circle, (a+bc)/2.
a(n) = (A046086(n) + A046087(n)  A020882(n))/2 = A087459(n)/2.
a(n) = sqrt{(A118961(n)*A118962(n)/2}.  Lekraj Beedassy, May 07 2006


CROSSREFS

For ordered values of (a+bc)/2 see A020888.
Cf. A046086, A046087, A020882, A087459.
Sequence in context: A057047 A101447 A119322 * A186286 A023821 A262332
Adjacent sequences: A014495 A014496 A014497 * A014499 A014500 A014501


KEYWORD

nonn


AUTHOR

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


EXTENSIONS

More terms from Asher Auel (asher.auel(AT)reed.edu) May 05 2000
Extended by Ray Chandler, Mar 09 2004


STATUS

approved



