

A014498


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


10



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

Ray Chandler, Table of n, a(n) for n = 1..10000
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



