A282341 Primes p of the form x^2 + y^2 such that q = (x^2 + 1)/y^2 is a prime less than p.

349, 1049, 1733, 33749, 53849, 79549, 135449, 381949, 535849, 558149, 692249, 1036349, 1156249, 1483549, 1871449, 2304349, 3097769, 6181349, 6411049, 8809049, 10355549, 11102249, 16401701, 16491521, 22867549, 26419769, 27457889, 30603049, 31728577, 34176557

Offset: 1

Author

Thomas Ordowski and Altug Alkan, Feb 12 2017

Keywords

• nonn

Comments

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

Primes p = q are A002496.

Examples

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

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Subsequence of A002313.

Cf. A002496, A031396.

Programs

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
Charles R Greathouse IV, Feb 14 2017