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

1,1

Comments

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

Primes p = q are A002496.

Links

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

Example

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

Prog

(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

Crossrefs

Subsequence of A002313.

Cf. A002496, A031396.

Sequence in context: A054824 A031420 A273530 * A285463 A138944 A043619

Adjacent sequences: A282338 A282339 A282340 * A282342 A282343 A282344

Keyword

nonn

Author

Thomas Ordowski and Altug Alkan, Feb 12 2017

Status

approved