A225570 - OEIS

%I #16 Aug 11 2013 15:33:06

%S 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 49,98,196,65,130,43,86,172,344,688,229,458,916,305,610,203,406,812,

%U 1624,541,1082,2164,721,1442,2884,961,1922,3844,7688,15376,5125,10250

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

%C 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 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 Multiples of 3 are ignored because after visiting a multiple of 3, subsequent terms can only double.

%H T. D. Noe, <a href="/A225570/b225570.txt">Table of n, a(n) for n = 1..1000</a>

%p A225570 := proc(n)

%p     local a;

%p     option remember;

%p     if n <= 4  then

%p         2^(n-1) ;

%p     else

%p         a := (procname(n-1)-1)/3 ;

%p         if type(a,'integer') and type(a,'odd') and modp(a,3) <> 0 then

%p             return a;

%p         else

%p             return procname(n-1)*2 ;

%p         end if;

%p     end if;

%p end proc: # _R. J. Mathar_, Aug 03 2013

%t 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 Cf. A014682, A070165.

%K nonn

%O 1,2

%A _David Spies_, Jul 29 2013