

A089001


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


18



1, 3, 6, 9, 21, 24, 27, 30, 33, 36, 42, 45, 66, 72, 75, 87, 93, 96, 99, 102, 105, 123, 132, 135, 153, 156, 162, 177, 186, 189, 201, 204, 219, 228, 237, 240, 255, 264, 273, 285, 297, 300, 306, 321, 324, 327, 351, 357, 360, 366, 375, 387, 393, 399, 405, 417, 423
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OFFSET

1,2


COMMENTS

All terms except the first one are multiples of 3.  Zak Seidov, Feb 24 2006
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
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


LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000


FORMULA

a(n)=((A090698(n)1)/2)^(1/2).
Starting with n=2, a(n)=3*A089008(n1).  Zak Seidov, Feb 24 2006


MATHEMATICA

Select[Range[500], PrimeQ[2#^2 + 1]&] (* Vincenzo Librandi, Jan 07 2013 *)


PROG

(MAGMA) [n: n in [1..500]  IsPrime(2*n^2+1)]; // Vincenzo Librandi, Jan 07 2013
(PARI) is(n)=isprime(2*n^2+1) \\ Charles R Greathouse IV, Feb 17 2017


CROSSREFS

Cf. A089008, A090612, A090698.
Sequence in context: A285215 A015938 A116614 * A215666 A050889 A327140
Adjacent sequences: A088998 A088999 A089000 * A089002 A089003 A089004


KEYWORD

nonn,easy


AUTHOR

N. J. A. Sloane, Dec 20 2003


STATUS

approved



