OFFSET
1,1
COMMENTS
These numbers are prime in Z but not in Z[sqrt(5)] nor in Z[phi] (where phi is the golden ratio), since (k - sqrt(5))(k + sqrt(5)) = ((k + 1) - 2*phi)((k - 1) + 2*phi) = k^2 - 5. - Alonso del Arte, Aug 27 2013
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..8000
P. De Geest, Palindromic Quasipronics of the form n(n+x)
Eric Weisstein's World of Mathematics, Near-Square Prime
EXAMPLE
31 is in the sequence as it is equal to 6^2 - 5.
59 is in the sequence since it is equal to 8^2 - 5.
95 is not in the sequence though it does equal 10^2 - 5.
MATHEMATICA
Select[Table[n^2 - 5, {n, 200}], PrimeQ] (* Harvey P. Dale, Jan 17 2011 *)
PROG
(Magma) [a: n in [1..300] | IsPrime(a) where a is n^2-5]; // Vincenzo Librandi, Dec 01 2011
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved