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A024892 Numbers n such that 3*n+1 is prime. 9

%I

%S 2,4,6,10,12,14,20,22,24,26,32,34,36,42,46,50,52,54,60,64,66,70,74,76,

%T 80,90,92,94,102,104,110,112,116,122,124,126,132,136,140,144,146,152,

%U 154,162,166,174,180,182,190,192,200,202,204,206,210,214,220,224,230,236,242,244,246

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

%C All the primes (with the exception of 3), can be expressed as 3*n+1 or 3*n-1. - _C├ęsar Aguilera_, Apr 13 2013

%C The associated prime A002476(n) has a unique representation as x^2 + x*y - 2*y^2 = (x + 2*y)*(x-y) 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

%H Vincenzo Librandi, <a href="/A024892/b024892.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) = (A002476(n) - 1)/3. See the name.

%F a(n) = 2*A024899(n) = A034936(n)+1

%t lst={}; Do[p=3*n+1; If[PrimeQ[p], AppendTo[lst, n]], {n, 0, 10^3}]; lst (* _Vladimir Joseph Stephan Orlovsky_, Sep 10 2008 *)

%t Select[Range[250], PrimeQ[3# + 1] &] (* _Vincenzo Librandi_, Sep 25 2012 *)

%o (MAGMA) [n: n in [1..1000] | IsPrime(3*n+1)]; // _Vincenzo Librandi_, Nov 20 2010

%Y Cf. A002476 (associated primes), A091178 (gives prime index).

%K nonn,easy

%O 1,1

%A _Clark Kimberling_

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Last modified September 30 04:15 EDT 2016. Contains 276618 sequences.