Search: id:A002476
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%I A002476 M4344 N1819
%S A002476 7,13,19,31,37,43,61,67,73,79,97,103,109,127,139,151,157,163,181,193,
%T A002476 199,211,223,229,241,271,277,283,307,313,331,337,349,367,373,379,397,
%U A002476 409,421,433,439,457,463,487,499,523,541,547,571,577,601,607,613,619
%N A002476 Primes of form 6n + 1.
%C A002476 Equivalently, primes of the form 3n + 1.
%C A002476 Primes p dividing sum(k=0,p,C(2k,k)) -3 = A006134(p)-3 - Benoit Cloitre 
               (benoit7848c(AT)orange.fr), Feb 08 2003
%C A002476 Primes p such that tau(p)==2 (mod 3) where tau(x) is the Ramanujan tau 
               function (cf. A000594). - Benoit Cloitre (benoit7848c(AT)orange.fr), 
               May 04 2003
%C A002476 Primes of the form x^2-xy+7y^2 with x and y nonnegative. - T. D. Noe 
               (noe(AT)sspectra.com), May 07 2005
%C A002476 Primes p such that p^2 divides Sum[Sum[(2k)!/(k!)^2,{k,1,m}],{m,1,2(p-1)}]. 
               - Alexander Adamchuk (alex(AT)kolmogorov.com), Jul 04 2006
%C A002476 A039701(A049084(a(n))) = A134323(A049084(a(n))) = 1. - Reinhard Zumkeller 
               (reinhard.zumkeller(AT)gmail.com), Oct 21 2007
%C A002476 The set of primes of the form 3n + 1 is a superset of the set of greater 
               of twin primes larger than five (A006512). - Paul Muljadi (paulmuljadi(AT)yahoo.com), 
               Jun 05 2008
%C A002476 Also primes p such that the arithmetic mean of divisors of p^2 is an 
               integer : sigma_1(p^2)/sigma_0(p^2) = C. (A000203(p^2)/A000005(p^2) 
               = C) [From Ctibor O. Zizka (c.zizka(AT)email.cz), Sep 15 2008]
%C A002476 Is this the same sequence as A139492?
%C A002476 Primes p such that arithmetic mean of divisors of p^2 is an integer. 
               [From Ctibor O. Zizka (c.zizka(AT)email.cz), Oct 20 2009]
%D A002476 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A002476 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A002476 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 A002476 K. G. Reuschle, Tafeln Complexer Primzahlen. K\"{o}nigl. Akademie der 
               Wissenschaften, Berlin, 1875, p. 1.
%H A002476 T. D. Noe, <a href="b002476.txt">Table of n, a(n) for n=1..1000</a>
%H A002476 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 A002476 C. Banderier, <a href="http://algo.inria.fr/banderier/Recipro/node18.html">
               Calcul de (-3/p)</a>
%H A002476 A. Granville and G. Martin, <a href="http://www.arXiv.org/abs/math.NT/
               0408319">Prime number races</a>
%p A002476 a := [ ]: for n from 1 to 400 do if isprime(6*n+1) then a := [ op(a), 
               n ]; fi; od: A002476 := n->a[n];
%t A002476 Select[6*Range[100] + 1, PrimeQ[ # ] &] - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), 
               Apr 06 2006
%o A002476 (PARI) \primes of the form 3n+1 f(n) = for(x=1,n,y=3*x + 1;if(isprime(y),
               print1(y","))) (from Cino Hilliard (hillcino368(AT)gmail.com), Feb 
               04 2004)
%Y A002476 Cf. A045331.
%Y A002476 For values of n see A024899. Primes of form 3n-1 give A003627.
%Y A002476 These are the primes arising in A024892, A024899, A034936, A091178 gives 
               prime index.
%Y A002476 Cf. A006512.
%Y A002476 Sequence in context: A038590 A129389 A107925 this_sequence A123365 A144921 
               A040079
%Y A002476 Adjacent sequences: A002473 A002474 A002475 this_sequence A002477 A002478 
               A002479
%K A002476 nonn,nice,easy
%O A002476 1,1
%A A002476 N. J. A. Sloane (njas(AT)research.att.com).

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