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A061419 a(n) = ceiling(a(n-1)*3/2) with a(1) = 1.

%I A061419 #64 Feb 16 2025 08:32:44
%S A061419 1,2,3,5,8,12,18,27,41,62,93,140,210,315,473,710,1065,1598,2397,3596,
%T A061419 5394,8091,12137,18206,27309,40964,61446,92169,138254,207381,311072,
%U A061419 466608,699912,1049868,1574802,2362203,3543305,5314958,7972437,11958656
%N A061419 a(n) = ceiling(a(n-1)*3/2) with a(1) = 1.
%C A061419 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
%D A061419 Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 2.30.1, p. 196.
%H A061419 Harry J. Smith, <a href="/A061419/b061419.txt">Table of n, a(n) for n = 1..500</a>
%H A061419 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 A061419 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 A061419 Don Knuth, <a href="http://cs.stanford.edu/~knuth/papers/ambidextrous.pdf">Ambidextrous Numbers</a>, Preprint, September 2022.
%H A061419 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 A061419 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PowerCeilings.html">Power Ceilings</a>.
%H A061419 <a href="/index/J#Josephus">Index entries for sequences related to the Josephus Problem</a>
%F A061419 a(n) = A061418(n) - 1 = floor(K*(3/2)^n) where K = 1.08151366859...
%F A061419 The constant K is (2/3)*K(3) (see A083286). - _Ralf Stephan_, May 29 2003
%F A061419 a(1) = 1, a(n) = A070885(n)/3. - _Benoit Cloitre_, Aug 18 2002
%F A061419 a(n) = ceiling((a(n-1) + a(n-2))*9/10) - _Franklin T. Adams-Watters_, May 01 2006
%e A061419 a(6) = ceiling(8*3/2) = 12.
%p A061419 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 A061419 a=1;a=Table[a=Ceiling[a*3/2],{n,0,4!}] (* _Vladimir Joseph Stephan Orlovsky_, Apr 13 2010 *)
%t A061419 NestList[Ceiling[3#/2]&,1,39] (* _Stefano Spezia_, Dec 08 2024 *)
%o A061419 (Magma) [ n eq 1 select 1 else Ceiling(Self(n-1)*3/2): n in [1..40] ]; // _Klaus Brockhaus_, Nov 14 2008
%o A061419 (PARI) { a=2/3; for (n=1, 500, write("b061419.txt", n, " ", a=ceil(a*3/2)) ) } \\ _Harry J. Smith_, Jul 22 2009
%o A061419 (Python)
%o A061419 from itertools import islice
%o A061419 def A061419_gen(): # generator of terms
%o A061419     a = 2
%o A061419     while True:
%o A061419         yield a-1
%o A061419         a += a>>1
%o A061419 A061419_list = list(islice(A061419_gen(),70)) # _Chai Wah Wu_, Sep 20 2022
%Y A061419 Cf. A002379, A003312, A034082, A061418, A061420, A070885, A083286.
%Y A061419 First differences are in A073941.
%K A061419 nonn
%O A061419 1,2
%A A061419 _Henry Bottomley_, May 02 2001