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A070885 a(n) = (3/2)*a(n-1) if a(n-1) is even; (3/2)*(a(n-1)+1) if a(n-1) is odd.

%I A070885 #64 Feb 16 2025 08:32:46
%S A070885 1,3,6,9,15,24,36,54,81,123,186,279,420,630,945,1419,2130,3195,4794,
%T A070885 7191,10788,16182,24273,36411,54618,81927,122892,184338,276507,414762,
%U A070885 622143,933216,1399824,2099736,3149604,4724406,7086609,10629915
%N A070885 a(n) = (3/2)*a(n-1) if a(n-1) is even; (3/2)*(a(n-1)+1) if a(n-1) is odd.
%C A070885 The smallest positive number such that A024629(a(n)) has n digits, per page 9 of the Tanton reference in Links. - _Glen Whitney_, Sep 17 2017
%D A070885 Wolfram, S. A New Kind of Science. Champaign, IL: Wolfram Media, 2002, p. 123.
%H A070885 Reinhard Zumkeller, <a href="/A070885/b070885.txt">Table of n, a(n) for n = 1..1000</a>
%H A070885 B. Chen, R. Chen, J. Guo, S. Lee et al., <a href="http://arxiv.org/abs/1808.04304">On Base 3/2 and its Sequences</a>, arXiv:1808.04304 [math.NT], 2018.
%H A070885 James Tanton, <a href="http://gdaymath.com/wp-content/uploads/2017/04/Chapter-9-EXPLODING-DOTS.pdf">Exploding Dots, Chapter 9</a>
%H A070885 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/WolframSequences.html">Wolfram Sequences</a>
%F A070885 For n > 1, a(n) = 3*A061419(n) = 3*floor(K*(3/2)^n) where K=1.08151366859... - _Benoit Cloitre_, Aug 18 2002
%F A070885 a(n) = 3*ceiling(a(n-1)/2). - _Benoit Cloitre_, Apr 25 2003
%F A070885 a(n+1) = a(n) + A081848(n), for n > 1. - _Reinhard Zumkeller_, Sep 05 2014
%p A070885 A070885 := proc(n)
%p A070885     option remember;
%p A070885     if n = 1 then
%p A070885         return 1;
%p A070885     elif type(procname(n-1),'even') then
%p A070885         procname(n-1) ;
%p A070885     else
%p A070885         procname(n-1)+1 ;
%p A070885     end if;
%p A070885     %*3/2 ;
%p A070885 end proc:
%p A070885 seq(A070885(n),n=1..80) ; # _R. J. Mathar_, Jun 18 2018
%t A070885 NestList[If[EvenQ[#],3/2 #,3/2 (#+1)]&,1,40] (* _Harvey P. Dale_, May 18 2018 *)
%o A070885 (Haskell)
%o A070885 a070885 n = a070885_list !! (n-1)
%o A070885 a070885_list = 1 : map (flip (*) 3 . flip div 2 . (+ 1)) a070885_list
%o A070885 -- _Reinhard Zumkeller_, Sep 05 2014
%o A070885 (Python)
%o A070885 from itertools import islice
%o A070885 def A070885_gen(): # generator of terms
%o A070885     a = 1
%o A070885     while True:
%o A070885         yield a
%o A070885         a += (a+1>>1)+(a&1)
%o A070885 A070885_list = list(islice(A070885_gen(),70)) # _Chai Wah Wu_, Sep 20 2022
%Y A070885 The constant K is 2/3*K(3) (see A083286). - _Ralf Stephan_, May 29 2003
%Y A070885 Cf. A003312.
%Y A070885 Cf. A081848.
%Y A070885 Cf. A205083 (parity of terms).
%K A070885 nonn
%O A070885 1,2
%A A070885 _Eric W. Weisstein_, May 14 2002