A048270 Sequence of 2 Pythagorean triangles, each with a leg and hypotenuse prime. The leg of the second triangle is the hypotenuse of the first.

3, 11, 19, 59, 271, 349, 521, 929, 1031, 1051, 1171, 2381, 2671, 2711, 2719, 3001, 3499, 3691, 4349, 4691, 4801, 4999, 5591, 5669, 6101, 6359, 6361, 7159, 7211, 7489, 8231, 8431, 8761, 9241, 10099, 10139, 11719, 11821, 12239, 12281, 12781

Offset: 1

Author

Harvey Dubner (harvey(AT)dubner.com)

Keywords

• nonn

Comments

It is conjectured that there are infinitely many such pairs of triangles.

Subsequence of A048161. - Lekraj Beedassy, Sep 16 2005

Examples

			p(1)=3 because 3 is prime, 5 = (3*3 + 1)/2 and 13 = (5*5 + 1)/2, 5, 13 both prime.
		

Links

• Ray Chandler, Table of n, a(n) for n = 1..10000
• H. Dubner and T. Forbes, Prime Pythagorean triangles, J. Integer Seqs., Vol. 4 (2001), #01.2.3.

Crossrefs

Cf. A048161, A048295, A308635, A308636. Primes in A116945.

Formula

For each p(n), there is a q=(p*p+1)/2 and r=(q*q+1)/2 such that p, q, r are all prime.

Extensions

More terms from Ray Chandler, Jun 12 2019