OFFSET
0,1
COMMENTS
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 S. Plewe, Dec 11 2007
Number of 2-sided prudent polygons of area n, for n>0, see Beaton, p. 5. - Jonathan Vos Post, Nov 30 2010
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..240
Nicholas R. Beaton, Philippe Flajolet, and Anthony J. Guttmann, The Enumeration of Prudent Polygons by Area and its Unusual Asymptotics, arXiv:1011.6195 [math.CO], Nov 29, 2010.
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 485
Popular Computing (Calabasas, CA), Sieves: Problem 43, Vol. 2 (No. 13, Apr 1974), pp. 6-7. This is Sieve #6 with K=2. [Annotated and scanned copy]
Eric Weisstein's World of Mathematics, Bertrand's Postulate
Index entries for linear recurrences with constant coefficients, signature (3,-2).
FORMULA
G.f.: (3-5*x)/((1-2*x)*(1-x)) = (3-5*x)/(1 - 3*x + 2*x^2) = 2/(1-x) + 1/(1-2*x).
a(0)=3, a(1)=4, a(n) = 3*a(n-1) - 2*a(n-2).
a(n) = A173786(n,1), for n>0. - Reinhard Zumkeller, Feb 28 2010
a(0)=3, a(n) = 2*a(n-1) - 2. - Vincenzo Librandi, Aug 06 2010
E.g.f.: (2 + exp(x))*exp(x). - Ilya Gutkovskiy, Aug 16 2016
MAPLE
spec := [S, {S=Union(Sequence(Union(Z, Z)), Sequence(Z), Sequence(Z))}, unlabeled]: seq(combstruct[count](spec, size=n), n=0..20);
MATHEMATICA
2^Range[0, 40]+2 (* Harvey P. Dale, Jun 26 2012 *)
PROG
(Magma) [2^n + 2: n in [0..35]]; // Vincenzo Librandi, Apr 29 2011
(PARI) a(n)=1<<n+2 \\ Charles R Greathouse IV, Nov 20 2011
(Haskell)
a052548 = (+ 2) . a000079
a052548_list = iterate ((subtract 2) . (* 2)) 3
-- Reinhard Zumkeller, Sep 05 2015
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
encyclopedia(AT)pommard.inria.fr, Jan 25 2000
EXTENSIONS
More terms from James A. Sellers, Jun 06 2000
STATUS
approved