A120890 Ordered odd leg of primitive Pythagorean triangles.

3, 5, 7, 9, 11, 13, 15, 15, 17, 19, 21, 21, 23, 25, 27, 29, 31, 33, 33, 35, 35, 37, 39, 39, 41, 43, 45, 45, 47, 49, 51, 51, 53, 55, 55, 57, 57, 59, 61, 63, 63, 65, 65, 67, 69, 69, 71, 73, 75, 75, 77, 77, 79, 81, 83, 85, 85, 87, 87, 89, 91, 91, 93, 93, 95, 95, 97, 99, 99, 101, 103

Offset: 1

Author

Lekraj Beedassy, Jul 12 2006

Keywords

• nonn

Comments

Ordered union of A081874 and A081934.

Conjecture: lim_{n->oo} a(n)/n = 1/Pi. Limit is also conjectured to be equal to lim_{n->oo} A120427(n)/n, see Selle reference, chapter 2.3.10. - Lothar Selle, Jun 21 2022

References

• Lothar Selle, Kleines Handbuch Pythagoreische Zahlentripel, Books on Demand, 4th impression 2022, chapter 2.2.1., see chapter 2.3.10 for identity of lim_{n->oo} A120427(n)/n.

Links

• Ray Chandler, Table of n, a(n) for n = 1..10000
• D. N. Lehmer, Asymptotic evaluation of certain totient sums, Amer. J. Math. 22, 293-335, 1900.
• F. Richman, Pythagorean Triangles

Crossrefs

Cf. A061346, A081874, A081934, A120891.

Cf. A120427.

Extensions

Corrected by T. D. Noe, Oct 25 2006