Search: id:A005385
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%I A005385 M3761
%S A005385 5,7,11,23,47,59,83,107,167,179,227,263,347,359,383,467,479,503,563,
%T A005385 587,719,839,863,887,983,1019,1187,1283,1307,1319,1367,1439,1487,1523,
%U A005385 1619,1823,1907,2027,2039,2063,2099,2207,2447,2459,2579,2819,2879,2903
%N A005385 Safe primes p: (p-1)/2 is also prime.
%C A005385 Then (p-1)/2 is called a Sophie Germain prime: see A005384.
%C A005385 Or, primes of the form 2p+1 where p is prime.
%C A005385 Primes p such that denominator(Bernoulli(p-1) + 1/p)=6. - Mohammed Bouayoun 
               (bouyao(AT)wanadoo.fr), Feb 10 2004
%C A005385 Or, primes p such that p-1 is a semiprime. - Zak Seidov (zakseidov(AT)yahoo.com), 
               Jul 01 2005
%C A005385 A156659(a(n)) = 1; A156875 gives numbers of safe primes <= n. [From Reinhard 
               Zumkeller (reinhard.zumkeller(AT)gmail.com), Feb 18 2009]
%C A005385 Near subset of A161897. [From Reikku Kulon (reikku(AT)gmail.com), Jun 
               21 2009]
%C A005385 Contribution from Daniel Forgues (squid(AT)zensearch.com), Jul 31 2009: 
               (Start)
%C A005385 A safe prime p is 7 or of the form 6k-1, k >= 1, i.e. p == 5 (mod 6).
%C A005385 A prime p of the form 6k+1, k >= 2, i.e. p = 1 (mod 6), cannot be a safe 
               prime since (p-1)/2 is composite and divisible by 3. (End)
%D A005385 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A005385 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.
%H A005385 T. D. Noe, <a href="b005385.txt">Table of n, a(n) for n=1..10000</a>
%H A005385 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 A005385 Wikipedia, <a href="http://en.wikipedia.org/wiki/Safe_prime">Safe prime</
               a>
%p A005385 with(numtheory); [ seq(safeprime(i),i=1..3000) ]: convert(%,set); convert(%,
               list); sort(%);
%t A005385 A005385=Select[Prime[Range[1000]], Plus@@Last/@FactorInteger[ #-1]==2&] 
               (Seidov)
%o A005385 (PARI) g(n) = forprime(x=2,n,y=x+x+1;if(isprime(y),print1(y","))) (Cino 
               Hilliard (hillcino368(AT)gmail.com), Sep 12 2004)
%Y A005385 a(n) = 2 * A005384(n) + 1.
%Y A005385 Cf. A007700, A023272, A023302, A023330, A057331, A005602.
%Y A005385 Except for the initial term, this is identical to A079148.
%Y A005385 Cf. A161897 [From Reikku Kulon (reikku(AT)gmail.com), Jun 21 2009]
%Y A005385 Sequence in context: A151715 A090810 A092307 this_sequence A075705 A141305 
               A067289
%Y A005385 Adjacent sequences: A005382 A005383 A005384 this_sequence A005386 A005387 
               A005388
%K A005385 nonn,easy,nice
%O A005385 1,1
%A A005385 N. J. A. Sloane (njas(AT)research.att.com).
%E A005385 More terms from Larry Reeves (larryr(AT)acm.org), Feb 15 2001

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