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%I M1388
%S 2,5,11,17,23,29,41,47,53,59,71,83,89,101,107,113,131,137,149,167,173,
%T 179,191,197,227,233,239,251,257,263,269,281,293,311,317,347,353,359,
%U 383,389,401,419,431,443,449,461,467,479,491,503,509,521,557,563,569,587
%N Primes of form 3n-1.
%C Primes p such that 1+x+x^2 is irreducible over GF(p). [Joerg Arndt, Aug 10 2011]
%C Primes p dividing sum(k=0,p,C(2k,k)) -1 = A006134(p)-1 - Benoit Cloitre, Feb 08 2003
%C A039701(A049084(a(n))) = 2; A134323(A049084(a(n))) = -1. - _Reinhard Zumkeller_, Oct 21 2007
%C The set of primes of the form 3n - 1 is a superset of the set of lesser of twin primes larger than three (A001359). - Paul Muljadi, Jun 05 2008
%C Primes of this form do not occur in or as divisors of {n^2+n+1}. See A002383 (n^2+n+1 = prime), A162471 (prime divisors of n^2+n+1 not in A002383), and A002061 (numbers of the form n^2-n+1). [From _Daniel Tisdale_, Jul 04 2009]
%C Or, primes not in A007645. A003627 UNION A007645 = A000040. Also, primes of the form 6*k-5/2-+3/2. [From Juri-Stepan Gerasimov, Jan 28 2010]
%C Except for first term "2", all these prime numbers are of the form: 6*n-1. - Vladimir Joseph Stephan Orlovsky, Jul 13 2011.
%C A088534(a(n)) = 0. [_Reinhard Zumkeller_, Oct 30 2011]
%C For n>1: Numbers k such that (k-4)! mod k =(-1)^(floor(k/3)+1)*floor((k+1)/6), k>4. [From Gary Detlefs, Jan 02 2012]
%C Binomial(a(n),3)/a(n)= (3*A024893(n)^2+A024893(n))/2, n>1. - Gary Detlefs, May 06 2012
%D M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 870.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H T. D. Noe, <a href="/A003627/b003627.txt">Table of n, a(n) for n = 1..1000</a>
%H M. Abramowitz and I. A. Stegun, eds., <a href="http://www.nrbook.com/abramowitz_and_stegun/">Handbook of Mathematical Functions</a>, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
%H A. Granville and G. Martin, <a href="http://www.arXiv.org/abs/math.NT/0408319">Prime number races</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/EisensteinPrime.html">Eisenstein Prime</a>
%F Sum_{n>=1} 1/a(n)^2 = 0.30792... = A085548 -1/9 - A175644. Sum_{n>=1} 1/a(n)^3 = 0.134125... = A085541 -1/27 - A175645. - R. J. Mathar, Apr 03 2011
%p t1 := {}; for n from 0 to 500 do if isprime(3*n+2) then t1 := {op(t1),3*n+2}; fi; od: A003627 := convert(t1,list);
%t lst={};Do[If[PrimeQ[p=3*n-1], (*Print[p];*)AppendTo[lst, p]], {n, 10^3}];lst [From Vladimir Orlovsky, Aug 21 2008]
%o (MAGMA) [n: n in PrimesUpTo(720) | n mod 3 eq 2]; // Bruno Berselli, Apr 05 2011
%o (Haskell)
%o a003627 n = a003627_list !! (n-1)
%o a003627_list = filter ((== 2) . (`mod` 3)) a000040_list
%o -- _Reinhard Zumkeller_, Oct 30 2011
%o (PARI) is(n)=n%3==2 && isprime(n) \\ _Charles R Greathouse IV_, Mar 20 2013
%Y Primes of form 3n+1 give A002476.
%Y These are the primes arising in A024893, A087370, A088879, A091177 gives prime index.
%Y Cf. A001359, A007645, A221717.
%Y Subsequence of A034020.
%K nonn,easy
%O 1,1
%A _N. J. A. Sloane_ and Mira Bernstein
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