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A282341
Primes p of the form x^2 + y^2 such that q = (x^2 + 1)/y^2 is a prime less than p.
1
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.
Sequence in context: A054824 A031420 A273530 * A285463 A138944 A043619
KEYWORD
nonn
AUTHOR
Thomas Ordowski and Altug Alkan, Feb 12 2017
STATUS
approved