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 A028870 Numbers k such that k^2 - 2 is prime. 36

%I

%S 2,3,5,7,9,13,15,19,21,27,29,33,35,37,43,47,49,55,61,63,69,71,75,77,

%T 89,93,103,107,117,119,121,127,131,135,139,145,155,161,169,173,177,

%U 183,191,205,211,217,223,231,233,237,239,247,253,257,259,265,267,273,279,285

%N Numbers k such that k^2 - 2 is prime.

%C It is conjectured that this sequence is infinite.

%C Primes 2,3,5,7,13,... are in A062326. - _Zak Seidov_, Oct 05 2014

%D D. Shanks, Solved and Unsolved Problems in Number Theory, 2nd. ed., Chelsea, 1978, p. 31.

%H Nathaniel Johnston, <a href="/A028870/b028870.txt">Table of n, a(n) for n = 1..10000</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>

%F a(n) = sqrt(2 + A028871(n)). - _Zak Seidov_, Oct 05 2014

%e 5^2 - 2 = 23 is prime, so 5 is in the sequence.

%p select(k->isprime(k^2-2),[\$1..300]); # _Muniru A Asiru_, Jul 15 2018

%t a[n_]:=n^x-y;lst={};x=2;y=2;Do[If[PrimeQ[a[n]],AppendTo[lst,n]],{n,0,6!}];lst (* _Vladimir Joseph Stephan Orlovsky_, Jan 03 2009 *)

%t Select[Range[300],PrimeQ[#^2-2]&] (* _Harvey P. Dale_, Mar 21 2013 *)

%o (MAGMA) [n: n in [1..1000] |IsPrime( n^2 - 2)]; // _Vincenzo Librandi_, Nov 18 2010

%o (PARI) is(n)=isprime(n^2-2) \\ _Charles R Greathouse IV_, Jul 01 2013

%Y Cf. A028871.

%K nonn,easy

%O 1,1

%A _Patrick De Geest_

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Last modified April 1 02:10 EDT 2020. Contains 333153 sequences. (Running on oeis4.)