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a(n) = ceiling(a(n-1)*3/2) with a(1) = 1.
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%I #58 Sep 21 2022 01:43:16

%S 1,2,3,5,8,12,18,27,41,62,93,140,210,315,473,710,1065,1598,2397,3596,

%T 5394,8091,12137,18206,27309,40964,61446,92169,138254,207381,311072,

%U 466608,699912,1049868,1574802,2362203,3543305,5314958,7972437,11958656

%N a(n) = ceiling(a(n-1)*3/2) with a(1) = 1.

%C 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

%H Harry J. Smith, <a href="/A061419/b061419.txt">Table of n, a(n) for n = 1..500</a>

%H Zakir Deniz, <a href="https://doi.org/10.1007/s00200-014-0245-0">Topology of acyclic complexes of tournaments and coloring</a>, Applicable Algebra in Engineering, Communication, March 2015, Volume 26, Issue 1-2, pp. 213-226.

%H A. Dubickas, <a href="https://doi.org/10.1017/S0017089508004655">On integer sequences generated by linear maps</a>, Glasg. Math. J. 51(2) (2009), 243-252.

%H Don Knuth, <a href="http://cs.stanford.edu/~knuth/papers/ambidextrous.pdf">Ambidextrous Numbers</a>, Preprint, September 2022.

%H A. M. Odlyzko and H. S. Wilf, <a href="https://doi.org/10.1017/S0017089500008272">Functional iteration and the Josephus problem</a>, Glasgow Math. J. 33(2) (1991), 235-240.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PowerCeilings.html">Power Ceilings</a>.

%H <a href="/index/J#Josephus">Index entries for sequences related to the Josephus Problem</a>

%F a(n) = A061418(n) - 1 = floor(K*(3/2)^n) where K = 1.08151366859...

%F The constant K is (2/3)*K(3) (see A083286). - _Ralf Stephan_, May 29 2003

%F a(1) = 1, a(n) = A070885(n)/3. - _Benoit Cloitre_, Aug 18 2002

%F a(n) = ceiling((a(n-1) + a(n-2))*9/10) - _Franklin T. Adams-Watters_, May 01 2006

%e a(6) = ceiling(8*3/2) = 12.

%p 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

%t a=1;a=Table[a=Ceiling[a*3/2],{n,0,4!}] (* _Vladimir Joseph Stephan Orlovsky_, Apr 13 2010 *)

%o (Magma) [ n eq 1 select 1 else Ceiling(Self(n-1)*3/2): n in [1..40] ]; // _Klaus Brockhaus_, Nov 14 2008

%o (PARI) { a=2/3; for (n=1, 500, write("b061419.txt", n, " ", a=ceil(a*3/2)) ) } \\ _Harry J. Smith_, Jul 22 2009

%o (Python)

%o from itertools import islice

%o def A061419_gen(): # generator of terms

%o a = 2

%o while True:

%o yield a-1

%o a += a>>1

%o A061419_list = list(islice(A061419_gen(),70)) # _Chai Wah Wu_, Sep 20 2022

%Y Cf. A002379, A003312, A034082, A061418, A061420, A070885, A083286.

%Y First differences are in A073941.

%K nonn

%O 1,2

%A _Henry Bottomley_, May 02 2001