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

1,1

Comments

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

Subsequence of A048161. - Lekraj Beedassy, Sep 16 2005

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.

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.

Example

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

Crossrefs

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

Sequence in context: A213051 A238362 A116945 * A183459 A176872 A088733

Adjacent sequences: A048267 A048268 A048269 * A048271 A048272 A048273

Keyword

nonn

Author

Harvey Dubner (harvey(AT)dubner.com)

Extensions

More terms from Ray Chandler, Jun 12 2019

Status

approved