0,1

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

a(n) = A058896(n)/A000918(n). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Feb 14 2009]

"Sieves", Popular Computing (Calabasas, CA), Vol. 2 (No. 13, Apr 1974), pp. 6-7; sieve #6 (K=2).

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 485

Index entries for sequences generated by sieves

Eric Weisstein's World of Mathematics, Bertrand's Postulate

G.f.: -(-3+5*x)/(-1+2*x)/(-1+x)

Recurrence: {a(0)=3, a(1)=4, -2*a(n)+a(n+1)+2}

spec := [S, {S=Union(Sequence(Union(Z, Z)), Sequence(Z), Sequence(Z))}, unlabeled]: seq(combstruct[count](spec, size=n), n=0..20);

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]

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]

(Other) sage: [gaussian_binomial(n, 1, 2)+3 for n in xrange(0, 32)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 31 2009]

Apart from initial term, same as A056469.

Cf. A003462, A007051, A034472, A024023, A067771, A029858, A134931, A115099, A100774, A079004, A058481 [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Dec 25 2008]

Sequence in context: A068922 A032408 A018908 this_sequence A103049 A103016 A061032

Adjacent sequences: A052545 A052546 A052547 this_sequence A052549 A052550 A052551

easy,nonn

encyclopedia(AT)pommard.inria.fr, Jan 25 2000

More terms from James A. Sellers (sellersj(AT)math.psu.edu), Jun 06 2000