Search: id:A003627
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%I A003627 M1388
%S A003627 2,5,11,17,23,29,41,47,53,59,71,83,89,101,107,113,131,137,149,167,173,
%T A003627 179,191,197,227,233,239,251,257,263,269,281,293,311,317,347,353,359,
%U A003627 383,389,401,419,431,443,449,461,467,479,491,503,509,521,557,563,569,587
%N A003627 Primes of form 3n-1.
%C A003627 Primes p dividing sum(k=0,p,C(2k,k)) -1 = A006134(p)-1 - Benoit Cloitre 
               (benoit7848c(AT)orange.fr), Feb 08 2003
%C A003627 A039701(A049084(a(n))) = 2; A134323(A049084(a(n))) = -1. - Reinhard Zumkeller 
               (reinhard.zumkeller(AT)gmail.com), Oct 21 2007
%C A003627 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 (paulmuljadi(AT)yahoo.com), 
               Jun 05 2008
%C A003627 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 (daniel6874(AT)gmail.com), Jul 04 2009]
%D A003627 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 A003627 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A003627 T. D. Noe, <a href="b003627.txt">Table of n, a(n) for n=1..1000</a>
%H A003627 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 A003627 A. Granville and G. Martin, <a href="http://www.arXiv.org/abs/math.NT/
               0408319">Prime number races</a>
%H A003627 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               EisensteinPrime.html">Eisenstein Prime</a>
%p A003627 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 A003627 lst={};Do[If[PrimeQ[p=3*n-1], (*Print[p];*)AppendTo[lst, p]], {n, 10^3}];
               lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Aug 21 2008]
%Y A003627 Primes of form 3n+1 give A002476.
%Y A003627 These are the primes arising in A024893, A087370, A088879, A091177 gives 
               prime index.
%Y A003627 Cf. A001359.
%Y A003627 Sequence in context: A164921 A156830 A140556 this_sequence A103203 A105875 
               A031368
%Y A003627 Adjacent sequences: A003624 A003625 A003626 this_sequence A003628 A003629 
               A003630
%K A003627 nonn,easy
%O A003627 1,1
%A A003627 N. J. A. Sloane (njas(AT)research.att.com) and Mira Bernstein

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