

A024892


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


13



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

Every prime (with the exception of 3) can be expressed as 3*k+1 or 3*k1.  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
For all elements of this sequence there are no (x,y) positive integers such that a(n) = 3*x*y + x + y or a(n) = 3*x*y  x  y.  Pedro Caceres, Jan 28 2021


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.
a(n) = A153183(n)  1 = A107303(n)  2.


MATHEMATICA

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).
Cf. A153183, A107303.
Sequence in context: A255056 A164875 A301646 * A087136 A015921 A232964
Adjacent sequences: A024889 A024890 A024891 * A024893 A024894 A024895


KEYWORD

nonn,easy


AUTHOR

Clark Kimberling


STATUS

approved



