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%I #21 Sep 08 2022 08:46:07
%S 2,7,11,17,29,35,37,43,53,55,65,73,79,83,97,115,119,125,133,137,155,
%T 161,169,187,191,205,209,233,251,263,269,271,277,281,287,295,335,343,
%U 359,361,379,385,389,395,407,413,425,433,451,461,475,479,493,505,511,521,529,541,559,577
%N Numbers n such that (n^2 + 2)/3 is prime.
%C If n == 1 mod 3, then (n - 1)/3 is in A086285.
%H Robert Israel, <a href="/A240878/b240878.txt">Table of n, a(n) for n = 1..10000</a>
%e (2^2 + 2)/3 = 6/3 = 2, which is prime, so 2 is in the sequence.
%e (7^2 + 2)/3 = 51/3 = 17, which is prime, so 7 is in the sequence.
%e (11^2 + 2)/3 = 123/3 = 41, which is prime, so 11 is in the sequence.
%e (13^2 + 2)/3 = 171/3 = 57 = 3 * 19, which is not prime, so 13 is not in the sequence.
%p N:= 10000; # to get all terms <= 3 N + 2
%p A240878:= select(t -> isprime((t^2+2)/3),{seq(seq(3*i+j,j=1..2),i=0..N)}):
%t Select[Range[500], PrimeQ[(#^2 + 2)/3] &] (* _Alonso del Arte_, Apr 13 2014 *)
%o (Magma) [2] cat [n: n in [4..600] | IsPrime((n^2 + 2) div 3)]; // _Vincenzo Librandi_, Jul 01 2014
%o (PARI) is(n)=isprime((n^2+2)/3) \\ _Charles R Greathouse IV_, Jun 06 2017
%Y Cf. A086285.
%K nonn,easy
%O 1,1
%A _Robert Israel_, Apr 13 2014
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