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A308341 Hypotenuses of primitive Pythagorean triangles two sides of which are Pythagorean primes.

%I A308341 #28 Jul 29 2019 12:23:01
%S A308341 13,421,1861,5101,16381,60901,83641,100801,106261,135721,161881,
%T A308341 205441,218461,337021,388081,431521,571381,637321,697381,926161,
%U A308341 1108561,1460341,1515541,1806901,1899301,2334961,2574181,2601481,2740141,2834581,2853661,3248701,3403441,3723721,3889261,4503001
%N A308341 Hypotenuses of primitive Pythagorean triangles two sides of which are Pythagorean primes.
%C A308341 Hypotenuses of primitive Pythagorean triangles of the form (2m+1, 2m^2+2m, 2m^2+2m+1), where the hypotenuse and longer leg differ by one.
%C A308341 Except for the first term a(n) is of the form 60k + 1, hence the longer leg is 60k. 60 is the largest number that always divides the product of the sides of any Pythagorean triangle.
%H A308341 Wikipedia, <a href="https://en.m.wikipedia.org/wiki/Pythagorean_triple">Pythagorean triple</a>
%e A308341 13 is a term because 13 and 5 are Pythagorean primes and are sides of {5,12,13}.
%e A308341 421 is a term because 421 and 29 are Pythagorean primes and are sides of {29,420,421}.
%e A308341 1861 is a term because 1861 and 61 are Pythagorean primes and are sides of {61,1860,1861}.
%e A308341 5101 is a term because 5101 and 101 are Pythagorean primes and are sides of {101,5100,5101}.
%o A308341 (PARI) hyp(n) = {return((2*((n-1)/2)^2) + (2*((n-1)/2)) + 1);}
%o A308341 lista(n) = forprime(p=2, n, if((p%4 == 1) && isprime(p) && isprime(hyp(p)), print1(hyp(p), ", ")));
%o A308341 lista(3100)
%Y A308341 Cf. A002144, A008846.
%Y A308341 Subset of A027862.
%K A308341 nonn
%O A308341 1,1
%A A308341 _Torlach Rush_, May 20 2019