

A024892


Numbers n such that 3*n+1 is prime.


9



2, 4, 6, 10, 12, 14, 20, 22, 24, 26, 32, 34, 36, 42, 46, 50, 52, 54, 60, 64, 66, 70, 74, 76, 80, 90, 92, 94, 102, 104, 110, 112, 116, 122, 124, 126, 132, 136, 140, 144, 146, 152, 154, 162, 166, 174, 180, 182, 190, 192, 200, 202, 204, 206, 210, 214, 220, 224, 230, 236, 242, 244, 246
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OFFSET

1,1


COMMENTS

All the primes (with the exception of 3), can be expressed as 3*n+1 or 3*n1.  César Aguilera, Apr 13 2013
The associated prime A002476(n) has a unique representation as x^2 + x*y  2*y^2 = (x + 2*y)*(xy) with positive integers, namely (x(n), y(n)) = (a(n) + 1, a(n)). See the N. J. A. Sloane, May 31 2014, comment on A002476.  Wolfdieter Lang, Feb 09 2016


LINKS

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


FORMULA

a(n) = (A002476(n)  1)/3. See the name.
a(n) = 2*A024899(n) = A034936(n)+1


MATHEMATICA

lst={}; Do[p=3*n+1; If[PrimeQ[p], AppendTo[lst, n]], {n, 0, 10^3}]; lst (* Vladimir Joseph Stephan Orlovsky, Sep 10 2008 *)
Select[Range[250], PrimeQ[3# + 1] &] (* Vincenzo Librandi, Sep 25 2012 *)


PROG

(MAGMA) [n: n in [1..1000]  IsPrime(3*n+1)]; // Vincenzo Librandi, Nov 20 2010
(PARI) is(n)=isprime(3*n+1) \\ Charles R Greathouse IV, Feb 17 2017


CROSSREFS

Cf. A002476 (associated primes), A091178 (gives prime index).
Sequence in context: A047410 A255056 A164875 * A087136 A015921 A232964
Adjacent sequences: A024889 A024890 A024891 * A024893 A024894 A024895


KEYWORD

nonn,easy


AUTHOR

Clark Kimberling


STATUS

approved



