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A225570 The greedy smallest infinite reverse Collatz (3x+1) sequence.

%I A225570 #16 Aug 11 2013 15:33:06
%S A225570 1,2,4,8,16,5,10,20,40,13,26,52,17,34,11,22,7,14,28,56,112,37,74,148,
%T A225570 49,98,196,65,130,43,86,172,344,688,229,458,916,305,610,203,406,812,
%U A225570 1624,541,1082,2164,721,1442,2884,961,1922,3844,7688,15376,5125,10250
%N A225570 The greedy smallest infinite reverse Collatz (3x+1) sequence.
%C A225570 For each a(n) (where n > 4), a(n) = (a(n-1) - 1)/3 if the result is an odd integer not divisible by 3. Otherwise a(n) = 2 * a(n-1).
%C A225570 Going backwards from any term a(n) to a(1), this is the Collatz sequence for a(n).  Furthermore, each term in the sequence is the smallest possible term (ignoring multiples of 3) with this property given the previous term.
%C A225570 Multiples of 3 are ignored because after visiting a multiple of 3, subsequent terms can only double.
%H A225570 T. D. Noe, <a href="/A225570/b225570.txt">Table of n, a(n) for n = 1..1000</a>
%p A225570 A225570 := proc(n)
%p A225570     local a;
%p A225570     option remember;
%p A225570     if n <= 4  then
%p A225570         2^(n-1) ;
%p A225570     else
%p A225570         a := (procname(n-1)-1)/3 ;
%p A225570         if type(a,'integer') and type(a,'odd') and modp(a,3) <> 0 then
%p A225570             return a;
%p A225570         else
%p A225570             return procname(n-1)*2 ;
%p A225570         end if;
%p A225570     end if;
%p A225570 end proc: # _R. J. Mathar_, Aug 03 2013
%t A225570 last = 8; Join[{1, 2, 4, 8}, Table[test = (last - 1)/3; If[OddQ[last] || ! IntegerQ[test] || IntegerQ[test/3], last = 2*last, last = (last - 1)/3]; last, {96}]] (* _T. D. Noe_, Aug 11 2013 *)
%Y A225570 Cf. A014682, A070165.
%K A225570 nonn
%O A225570 1,2
%A A225570 _David Spies_, Jul 29 2013