A282341 - OEIS

A282341

Primes p of the form x^2 + y^2 such that q = (x^2 + 1)/y^2 is a prime less than p.

%I #12 Feb 14 2017 19:06:03

%S 349,1049,1733,33749,53849,79549,135449,381949,535849,558149,692249,

%T 1036349,1156249,1483549,1871449,2304349,3097769,6181349,6411049,

%U 8809049,10355549,11102249,16401701,16491521,22867549,26419769,27457889,30603049,31728577,34176557

%N Primes p of the form x^2 + y^2 such that q = (x^2 + 1)/y^2 is a prime less than p.

%C The negative Pell equation x^2 - q*y^2 = -1, hence q = (x^2 + 1)/y^2.

%C Primes p = q are A002496.

%H Charles R Greathouse IV, <a href="/A282341/b282341.txt">Table of n, a(n) for n = 1..10000</a>

%e For prime p = 349 = 18^2 + 5^2 is q = (18^2 + 1)/5^2 = 13 prime < p.

%o (PARI) list(lim)=my(v=List(),x2,q,y,p); for(x=1,sqrtint(lim\4), x2=4*x^2; [q,y]=core(x2+1,1); p=x2+y^2; if(q<p && p<=lim && isprime(q) && isprime(p), listput(v,p))); Set(v) \\ _Charles R Greathouse IV_, Feb 14 2017

%Y Subsequence of A002313.

%Y Cf. A002496, A031396.

%K nonn

%O 1,1

%A _Thomas Ordowski_ and _Altug Alkan_, Feb 12 2017