A156682 Consider all Pythagorean triangles A^2 + B^2 = C^2 with AA009004(n)).

5, 13, 10, 25, 17, 15, 41, 26, 61, 20, 37, 85, 50, 25, 39, 113, 34, 65, 145, 30, 82, 181, 29, 52, 101, 35, 75, 221, 122, 265, 40, 51, 74, 145, 65, 313, 170, 45, 123, 365, 53, 100, 197, 421, 50, 78, 226, 481, 68, 130, 257, 55, 65, 183, 545, 290, 91, 125, 613, 60, 85, 111

Offset: 1

Author

Ant King, Feb 17 2009

Keywords

• easy
• nice
• nonn

Comments

The corresponding sequence for primitive triples is A156679. For all triples, the ordered sequence of C values is A020882 (allowing repetitions) and A009003 (excluding repetitions).

Examples

			As the first four Pythagorean triples (ordered by increasing A) are (3,4,5), (5,12,13), (6,8,10) and (7,24,25), then a(1)=5, a(2)=13, a(3)=10 and a(4)=25.
		

References

• Beiler, Albert H.: Recreations In The Theory Of Numbers, Chapter XIV, The Eternal Triangle, Dover Publications Inc., New York, 1964, pp. 104-134.
• Sierpinski, W.; Pythagorean Triangles, Dover Publications, Inc., Mineola, New York, 2003.

Links

• Ron Knott, Right-angled Triangles and Pythagoras' Theorem

Crossrefs

Cf. A009004, A156681, A156679, A020882, A009003.

Programs

Mathematica

PythagoreanTriplets[n_]:=Module[{t={{3,4,5}},i=4,j=5},While[i
				

Formula

a(n) = sqrt(A009004(n)^2 + A156681(n)^2).