A156679 Consider primitive Pythagorean triangles (A^2 + B^2 = C^2, gcd (A, B) = 1, A < BA020884(n)).

5, 13, 25, 17, 41, 61, 37, 85, 113, 65, 145, 181, 29, 101, 221, 265, 145, 313, 365, 53, 197, 421, 481, 257, 65, 545, 613, 85, 325, 685, 89, 761, 401, 841, 925, 125, 485, 1013, 1105, 73, 577, 1201, 149, 1301, 173, 677, 1405, 1513, 785, 185, 1625, 1741, 109, 229

Offset: 1

Author

Ant King, Feb 15 2009

Keywords

• easy
• nice
• nonn

Comments

The ordered sequence of A values is A020884(n) and the ordered sequence of C values is A020882(n) (allowing repetitions) and A008846(n) (excluding repetitions).

Examples

			As the first four primitive Pythagorean triples (ordered by increasing A) are (3,4,5), (5,12,13), (7,24,25) and (8,15,17), then a(1)=5, a(2)=13, a(3)=25 and a(4)=17.
		

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

• Reinhard Zumkeller, Table of n, a(n) for n = 1..1000
• Ron Knott, Right-angled Triangles and Pythagoras' Theorem

Crossrefs

Cf. A020884, A020882, A008846, A156678, A156682.

Cf. A037213.

Programs

Haskell

a156679 n = a156679_list !! (n-1)
a156679_list = f 1 1 where
   f u v | v > uu `div` 2        = f (u + 1) (u + 2)
         | gcd u v > 1 || w == 0 = f u (v + 2)
         | otherwise             = w : f u (v + 2)
         where uu = u ^ 2; w = a037213 (uu + v ^ 2)
-- Reinhard Zumkeller, Nov 09 2012

Mathematica

PrimitivePythagoreanTriplets[n_]:=Module[{t={{3,4,5}},i=4,j=5},While[iHarvey P. Dale, May 10 2020 *)