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A061419 a(n) = ceiling(a(n-1)*3/2) with a(1) = 1. 31
1, 2, 3, 5, 8, 12, 18, 27, 41, 62, 93, 140, 210, 315, 473, 710, 1065, 1598, 2397, 3596, 5394, 8091, 12137, 18206, 27309, 40964, 61446, 92169, 138254, 207381, 311072, 466608, 699912, 1049868, 1574802, 2362203, 3543305, 5314958, 7972437, 11958656 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
It appears that this sequence is the (L)-sieve transform of {3,6,9,12,...,3n,...} = A008585. (See A152009 for the definition of the (L)-sieve transform.) - John W. Layman, Jan 06 2009
LINKS
Zakir Deniz, Topology of acyclic complexes of tournaments and coloring, Applicable Algebra in Engineering, Communication, March 2015, Volume 26, Issue 1-2, pp. 213-226.
A. Dubickas, On integer sequences generated by linear maps, Glasg. Math. J. 51(2) (2009), 243-252.
Don Knuth, Ambidextrous Numbers, Preprint, September 2022.
A. M. Odlyzko and H. S. Wilf, Functional iteration and the Josephus problem, Glasgow Math. J. 33(2) (1991), 235-240.
Eric Weisstein's World of Mathematics, Power Ceilings.
FORMULA
a(n) = A061418(n) - 1 = floor(K*(3/2)^n) where K = 1.08151366859...
The constant K is (2/3)*K(3) (see A083286). - Ralf Stephan, May 29 2003
a(1) = 1, a(n) = A070885(n)/3. - Benoit Cloitre, Aug 18 2002
a(n) = ceiling((a(n-1) + a(n-2))*9/10) - Franklin T. Adams-Watters, May 01 2006
EXAMPLE
a(6) = ceiling(8*3/2) = 12.
MAPLE
a:=proc(n) option remember: if n=1 then 1 else ceil(procname(n-1)*3/2) fi; end; seq(a(n), n=1..40); # Muniru A Asiru, Jun 07 2018
MATHEMATICA
a=1; a=Table[a=Ceiling[a*3/2], {n, 0, 4!}] (* Vladimir Joseph Stephan Orlovsky, Apr 13 2010 *)
PROG
(Magma) [ n eq 1 select 1 else Ceiling(Self(n-1)*3/2): n in [1..40] ]; // Klaus Brockhaus, Nov 14 2008
(PARI) { a=2/3; for (n=1, 500, write("b061419.txt", n, " ", a=ceil(a*3/2)) ) } \\ Harry J. Smith, Jul 22 2009
(Python)
from itertools import islice
def A061419_gen(): # generator of terms
a = 2
while True:
yield a-1
a += a>>1
A061419_list = list(islice(A061419_gen(), 70)) # Chai Wah Wu, Sep 20 2022
CROSSREFS
First differences are in A073941.
Sequence in context: A109537 A081226 A156623 * A130732 A018135 A065435
KEYWORD
nonn
AUTHOR
Henry Bottomley, May 02 2001
STATUS
approved

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Last modified February 21 09:14 EST 2024. Contains 370228 sequences. (Running on oeis4.)