login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 (list; graph; refs; listen; history; text; internal format)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 25 12:18 EDT 2020. Contains 337343 sequences. (Running on oeis4.)