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Numbers k such that k^2 + 4 is prime.
(Formerly M2416)
28

%I M2416 #42 Sep 08 2022 08:44:35

%S 1,3,5,7,13,15,17,27,33,35,37,45,47,57,65,67,73,85,87,95,97,103,115,

%T 117,125,135,137,147,155,163,167,177,183,193,203,207,215,217,233,235,

%U 243,245,253,255,265,267,275,277,287,293,303,307,313,317,347,357,373,375

%N Numbers k such that k^2 + 4 is prime.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Vincenzo Librandi, <a href="/A007591/b007591.txt">Table of n, a(n) for n = 1..1000</a>

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

%t lst={};Do[If[PrimeQ[n^2+4], Print[n];AppendTo[lst, n]], {n, 10^5}];lst (* _Vladimir Joseph Stephan Orlovsky_, Aug 21 2008 *)

%t Select[Range[0, 400], PrimeQ[#^2 + 4] &] (* _Vincenzo Librandi_, Sep 25 2012 *)

%o (Magma) [n: n in [0..400] | IsPrime(n^2+4)]; // _Vincenzo Librandi_, Nov 18 2010

%o (PARI) select(n->isprime(n^2+4),vector(500,n,2*n-1)) \\ _Charles R Greathouse IV_, Sep 25 2012

%Y Other sequences of the type "Numbers k such that k^2 + i is prime": A005574 (i=1), A067201 (i=2), A049422 (i=3), this sequence (i=4), A078402 (i=5), A114269 (i=6), A114270 (i=7), A114271 (i=8), A114272 (i=9), A114273 (i=10), A114274 (i=11), A114275 (i=12).

%K nonn,easy

%O 1,2

%A _N. J. A. Sloane_, _R. K. Guy_