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A028877 Primes of form k^2 - 5. 3

%I

%S 11,31,59,139,191,251,479,571,1019,1151,1291,1439,1759,1931,2111,2699,

%T 3359,4091,5179,5471,6079,6719,8831,10399,12539,13451,14879,17419,

%U 20731,23099,26891,27551,28219,30271,30971,33119,33851,34591

%N Primes of form k^2 - 5.

%C 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

%H Vincenzo Librandi, <a href="/A028877/b028877.txt">Table of n, a(n) for n = 1..8000</a>

%H P. De Geest, <a href="http://www.worldofnumbers.com/consemor.htm">Palindromic Quasipronics of the form n(n+x)</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Near-SquarePrime.html">Near-Square Prime</a>

%e 31 is in the sequence as it is equal to 6^2 - 5.

%e 59 is in the sequence since it is equal to 8^2 - 5.

%e 95 is not in the sequence though it does equal 10^2 - 5.

%t Select[Table[n^2 - 5, {n, 200}], PrimeQ] (* _Harvey P. Dale_, Jan 17 2011 *)

%o (MAGMA) [a: n in [1..300] | IsPrime(a) where a is n^2-5]; // _Vincenzo Librandi_, Dec 01 2011

%Y Cf. A028875 (superset), A028876.

%K nonn,easy

%O 1,1

%A _Patrick De Geest_

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Last modified March 31 16:23 EDT 2020. Contains 333151 sequences. (Running on oeis4.)