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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
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
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
Sequence in context: A213051 A238362 A116945 * A183459 A176872 A088733
KEYWORD
nonn
AUTHOR
Harvey Dubner (harvey(AT)dubner.com)
EXTENSIONS
More terms from Ray Chandler, Jun 12 2019
STATUS
approved