

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.


7



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
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OFFSET

1,1


COMMENTS

It is conjectured that there is an infinite number of 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



