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A089001
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Numbers n such that 2*n^2 + 1 is prime.
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18
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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
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1,2
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COMMENTS
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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
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 1..1000
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FORMULA
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a(n)=((A090698(n)-1)/2)^(1/2).
Starting with n=2, a(n)=3*A089008(n-1). - Zak Seidov, Feb 24 2006
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MATHEMATICA
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Select[Range[500], PrimeQ[2#^2 + 1]&] (* Vincenzo Librandi, Jan 07 2013 *)
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PROG
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(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
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CROSSREFS
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Cf. A089008, A090612, A090698.
Sequence in context: A285215 A015938 A116614 * A215666 A050889 A327140
Adjacent sequences: A088998 A088999 A089000 * A089002 A089003 A089004
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane, Dec 20 2003
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STATUS
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approved
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