Search: id:A052548
Results 1-1 of 1 results found.

%I A052548
%S A052548 3,4,6,10,18,34,66,130,258,514,1026,2050,4098,8194,16386,32770,65538,
%T A052548 131074,262146,524290,1048578,2097154,4194306,8388610,16777218,
%U A052548 33554434,67108866,134217730,268435458,536870914,1073741826,2147483650
%N A052548 2^n+2.
%C A052548 The most "compact" sequence that satisfies Bertrand's Postulate. Begin 
               with a(1) = 3 = n, then 2n - 2 = 4 = n_1, 2n_1 - 2 = 6 = n_2, 2n_2 
               - 2 = 10, etc. = a(n), hence there is guaranteed to be at least one 
               prime between successive members of the sequence. - Andrew Plewe 
               (aplewe(AT)sbcglobal.net), Dec 11 2007
%C A052548 a(n) = A058896(n)/A000918(n). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Feb 14 2009]
%D A052548 "Sieves", Popular Computing (Calabasas, CA), Vol. 2 (No. 13, Apr 1974), 
               pp. 6-7; sieve #6 (K=2).
%H A052548 INRIA Algorithms Project, <a href="http://algo.inria.fr/bin/encyclopedia?Search=ECSnb&argsearch=485">
               Encyclopedia of Combinatorial Structures 485</a>
%H A052548 <a href="Sindx_Si.html#sieve">Index entries for sequences generated by 
               sieves</a>
%H A052548 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               BertrandsPostulate.html">Bertrand's Postulate</a>
%F A052548 G.f.: -(-3+5*x)/(-1+2*x)/(-1+x)
%F A052548 Recurrence: {a(0)=3, a(1)=4, -2*a(n)+a(n+1)+2}
%F A052548 a(n)=2*a(n-1)-2 (with a(1)=3) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), 
               Dec 01 2009]
%e A052548 For n=2, a(2)=2*3-2=4; n=3, a(3)=2*4-2=6. n=4, a(4)=2*6-2=10 [From Vincenzo 
               Librandi (vincenzo.librandi(AT)tin.it), Dec 01 2009]
%p A052548 spec := [S,{S=Union(Sequence(Union(Z,Z)),Sequence(Z),Sequence(Z))},unlabeled]: 
               seq(combstruct[count](spec,size=n), n=0..20);
%p A052548 g:=1/(1-2*z): gser:=series(g, z=0, 43): seq(coeff(gser, z, n)+2, n=0..31);
               # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 09 2009]
%t A052548 a=3;lst={a};Do[a=a*2-2;AppendTo[lst,a],{n,0,5!}];lst [From Vladimir Orlovsky 
               (4vladimir(AT)gmail.com), Dec 25 2008]
%o A052548 (Other) sage: [gaussian_binomial(n,1,2)+3 for n in xrange(0,32)] # [From 
               Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 31 2009]
%Y A052548 Apart from initial term, same as A056469.
%Y A052548 Cf. A003462, A007051, A034472, A024023, A067771, A029858, A134931, A115099, 
               A100774, A079004, A058481 [From Vladimir Orlovsky (4vladimir(AT)gmail.com), 
               Dec 25 2008]
%Y A052548 Sequence in context: A068922 A032408 A018908 this_sequence A103049 A103016 
               A061032
%Y A052548 Adjacent sequences: A052545 A052546 A052547 this_sequence A052549 A052550 
               A052551
%K A052548 easy,nonn,new
%O A052548 0,1
%A A052548 encyclopedia(AT)pommard.inria.fr, Jan 25 2000
%E A052548 More terms from James A. Sellers (sellersj(AT)math.psu.edu), Jun 06 2000

Search completed in 0.002 seconds