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Sequence of 2 Pythagorean triangles, each with a leg and hypotenuse prime. The leg of the second triangle is the hypotenuse of the first.
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%I #27 Feb 21 2022 02:17:44

%S 3,11,19,59,271,349,521,929,1031,1051,1171,2381,2671,2711,2719,3001,

%T 3499,3691,4349,4691,4801,4999,5591,5669,6101,6359,6361,7159,7211,

%U 7489,8231,8431,8761,9241,10099,10139,11719,11821,12239,12281,12781

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

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

%C Subsequence of A048161. - _Lekraj Beedassy_, Sep 16 2005

%H Ray Chandler, <a href="/A048270/b048270.txt">Table of n, a(n) for n = 1..10000</a>

%H H. Dubner and T. Forbes, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL4/DUBNER/pyth.html">Prime Pythagorean triangles</a>, J. Integer Seqs., Vol. 4 (2001), #01.2.3.

%F 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.

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

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

%K nonn

%O 1,1

%A Harvey Dubner (harvey(AT)dubner.com)

%E More terms from _Ray Chandler_, Jun 12 2019