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

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

Offset: 1

Author

N. J. A. Sloane, Dec 20 2003

Keywords

• nonn
• easy

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

Crossrefs

Cf. A089008, A090612, A090698.

Programs

Magma

[n: n in [1..500] | IsPrime(2*n^2+1)]; // Vincenzo Librandi, Jan 07 2013

Mathematica

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

PARI

is(n)=isprime(2*n^2+1) \\ Charles R Greathouse IV, Feb 17 2017

Formula

a(n)=((A090698(n)-1)/2)^(1/2).

Starting with n=2, a(n)=3*A089008(n-1). - Zak Seidov, Feb 24 2006