cp's OEIS Frontend

A089001 Numbers n such that 2*n^2 + 1 is prime.

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