A014498 Varying radii of inscribed circles within primitive Pythagorean triples as a function of increasing values of hypotenuse.

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

Offset: 1

Author

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

Keywords

• nonn

Links

• Ray Chandler, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Pythagorean Triple.
• Saltire Software, Pythagorean Triples

Crossrefs

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

Cf. A046086, A046087, A020882, A087459.

Formula

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.

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

Extensions

More terms from Asher Auel May 05 2000

Extended by Ray Chandler, Mar 09 2004