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%I #36 Sep 08 2022 08:45:12
%S 1,3,6,9,21,24,27,30,33,36,42,45,66,72,75,87,93,96,99,102,105,123,132,
%T 135,153,156,162,177,186,189,201,204,219,228,237,240,255,264,273,285,
%U 297,300,306,321,324,327,351,357,360,366,375,387,393,399,405,417,423
%N Numbers n such that 2*n^2 + 1 is prime.
%C All terms except the first one are multiples of 3. - _Zak Seidov_, Feb 24 2006
%C And because of this, all the primes except for the first one are congruent to 1 (mod 6). - _Robert G. Wilson v_, Aug 05 2014
%C For any n in this sequence, 3*(2*n^2 + 1) has the same nonzero digits as its prime factors in base 2n. - _Ely Golden_, Dec 12 2016
%H Vincenzo Librandi, <a href="/A089001/b089001.txt">Table of n, a(n) for n = 1..1000</a>
%F a(n)=((A090698(n)-1)/2)^(1/2).
%F Starting with n=2, a(n)=3*A089008(n-1). - _Zak Seidov_, Feb 24 2006
%t Select[Range[500], PrimeQ[2#^2 + 1]&] (* _Vincenzo Librandi_, Jan 07 2013 *)
%o (Magma) [n: n in [1..500] | IsPrime(2*n^2+1)]; // _Vincenzo Librandi_, Jan 07 2013
%o (PARI) is(n)=isprime(2*n^2+1) \\ _Charles R Greathouse IV_, Feb 17 2017
%Y Cf. A089008, A090612, A090698.
%K nonn,easy
%O 1,2
%A _N. J. A. Sloane_, Dec 20 2003
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