A156681 Consider all Pythagorean triangles A^2 + B^2 = C^2 with A < B < C; sequence gives values of B, sorted to correspond to increasing A (A009004).

4, 12, 8, 24, 15, 12, 40, 24, 60, 16, 35, 84, 48, 20, 36, 112, 30, 63, 144, 24, 80, 180, 21, 48, 99, 28, 72, 220, 120, 264, 32, 45, 70, 143, 60, 312, 168, 36, 120, 364, 45, 96, 195, 420, 40, 72, 224, 480, 60, 126, 255, 44, 56, 180, 544, 288, 84, 120, 612, 48, 77, 105

Offset: 1

Author

Ant King, Feb 17 2009

Keywords

• easy
• nice
• nonn

Comments

The ordered sequence of B values is A009012(n) (allowing repetitions) and A009023(n) (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)=4, a(2)=12, a(3)=8 and a(4)=24.
		

References

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

Links

• Shujing Lyu, Table of n, a(n) for n = 1..5000
• Ron Knott, Right-angled Triangles and Pythagoras' Theorem
• Robert Recorde, The Whetstone of Witte, whiche is the seconde parte of Arithmeteke: containing the extraction of rootes; the cossike practise, with the rule of equation; and the workes of Surde Nombers, London, 1557. See p. 57.

Crossrefs

Cf. A156682, A009004, A009012, A009023.

Programs

Mathematica

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

Formula

a(n) = sqrt(A156682(n)^2 - A009004(n)^2).