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Numbers n such that 2*(n^2 + 2) - 1 and 2*(n^2 + 2) + 1 are both prime.
2

%I #21 Sep 08 2022 08:46:09

%S 0,1,2,7,23,47,98,208,268,278,352,422,712,803,833,887,1022,1048,1052,

%T 1057,1297,1372,1517,1603,1657,1717,1748,1888,1988,2102,2207,2233,

%U 2357,2548,2567,2753,2828,2893,2938,3017,3362,3367,3572,3817,3908,4247,4268,4312,4403,4408,4412,4478

%N Numbers n such that 2*(n^2 + 2) - 1 and 2*(n^2 + 2) + 1 are both prime.

%C Numbers n such that 2*n^2 + 3 and 2*n^2 + 5 are both prime.

%H Harvey P. Dale, <a href="/A247175/b247175.txt">Table of n, a(n) for n = 1..1000</a>

%e 2 is in this sequence because 2*2^2 + 3 = 11 and 2*2^2 + 5 = 13 are both prime.

%t a247175[n_Integer] := Select[Range[n], And[PrimeQ[2*(#^2 + 2) - 1], PrimeQ[2*(#^2 + 2) + 1]] &]; a247175[4500] (* _Michael De Vlieger_, Nov 30 2014 *)

%t Select[Range[0,4500],AllTrue[2#^2+{3,5},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Feb 09 2019 *)

%o (Magma) [ n: n in [0..4500] | IsPrime(2*(n^2+2)-1) and IsPrime(2*(n^2+2)+1) ];

%Y Cf. A246079, A246699, A247197.

%K nonn

%O 1,3

%A _Juri-Stepan Gerasimov_, Nov 30 2014