login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A079796 Primes p such that (3*p)^2 + p^2 + 3^2 and (3*p)^2 - p^2 - 3^2 are both prime. 1
7, 29, 83, 181, 197, 337, 601, 631, 1303, 1847, 2029, 3023, 3109, 3359, 4591, 4649, 4831, 6397, 6791, 7489, 7559, 7573, 7951, 8609, 8933, 9857, 10151, 10457, 10501, 10709, 11467, 11633, 12011, 12377, 12641, 12739, 13469, 14197, 14449, 14519 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Also called nonomatic primes. There is probably an infinity of them. There seems to be no prime number with a similar property using 5 or a larger factor in the polynomials.

LINKS

Vincenzo Librandi and Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 (first 1000 terms from Librandi)

EXAMPLE

a(2) = 29 since (3*29)^2 + 29^2 + 3^2 = 8419 and (3*29)^2 - 29^2 - 3^2 = 6719 are both primes.

MATHEMATICA

Select[Prime@Range[1, 2000], PrimeQ[9 #^2 + #^2 + 9] && PrimeQ[9 #^2 - #^2 - 9] &] (* Vincenzo Librandi, Oct 18 2012 *)

PROG

(MAGMA) [p: p in PrimesUpTo(15000)| IsPrime( (3*p)^2 + p^2 + 3^2) and IsPrime((3*p)^2 - p^2 - 3^2)]; // Vincenzo Librandi, Oct 18 2012

(PARI) is(n)=isprime(10*n^2+9) && isprime(8*n^2-9) && isprime(n) \\ Charles R Greathouse IV, Jun 10 2015

CROSSREFS

Sequence in context: A231988 A141854 A267290 * A242727 A229795 A114043

Adjacent sequences:  A079793 A079794 A079795 * A079797 A079798 A079799

KEYWORD

easy,nonn

AUTHOR

Olivier Gérard, Feb 19 2003

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 October 17 04:09 EDT 2019. Contains 328106 sequences. (Running on oeis4.)