A308341 - OEIS

%I #28 Jul 29 2019 12:23:01

%S 13,421,1861,5101,16381,60901,83641,100801,106261,135721,161881,

%T 205441,218461,337021,388081,431521,571381,637321,697381,926161,

%U 1108561,1460341,1515541,1806901,1899301,2334961,2574181,2601481,2740141,2834581,2853661,3248701,3403441,3723721,3889261,4503001

%N Hypotenuses of primitive Pythagorean triangles two sides of which are Pythagorean primes.

%C 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 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 Wikipedia, <a href="https://en.m.wikipedia.org/wiki/Pythagorean_triple">Pythagorean triple</a>

%e 13 is a term because 13 and 5 are Pythagorean primes and are sides of {5,12,13}.

%e 421 is a term because 421 and 29 are Pythagorean primes and are sides of {29,420,421}.

%e 1861 is a term because 1861 and 61 are Pythagorean primes and are sides of {61,1860,1861}.

%e 5101 is a term because 5101 and 101 are Pythagorean primes and are sides of {101,5100,5101}.

%o (PARI) hyp(n) = {return((2*((n-1)/2)^2) + (2*((n-1)/2)) + 1);}

%o lista(n) = forprime(p=2, n, if((p%4 == 1) && isprime(p) && isprime(hyp(p)), print1(hyp(p), ", ")));

%o lista(3100)

%Y Cf. A002144, A008846.

%Y Subset of A027862.

%K nonn

%O 1,1

%A _Torlach Rush_, May 20 2019