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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 (list; graph; refs; listen; history; text; internal format)
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,changed

AUTHOR

Harvey Dubner (harvey(AT)dubner.com)

EXTENSIONS

More terms from Ray Chandler, Jun 12 2019

STATUS

approved

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Last modified June 17 16:56 EDT 2019. Contains 324196 sequences. (Running on oeis4.)