%I #9 Jan 17 2013 14:40:41

%S 1,10,10000101,100,100001,100001010,10000100010010101,1000,

%T 10000100010010101001,1000010,100001000100101,1000010100,1000010001,

%U 100001000100101010,100001000001010101,10000,1000010001001,100001000100101010010,100001000100101000101,10000100

%N The Collatz (3x+1) iteration mod 2 with bits combined.

%C This is essentially sequence A070165 mod 2 with bits in the same iteration combined. Note that A176999 is similar, but with a different encoding.

%C It appears that all numbers are distinct. Sequence A005186 tells how many numbers produce bit strings of a given length. Sequence A221468 converts to decimal and A221467 sorts them.

%H T. D. Noe, <a href="/A220145/b220145.txt">Table of n, a(n) for n = 1..10000</a>

%e For n = 7, the Collatz iteration is 7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1. Looking at these numbers in base 2 and reversing them, we obtain 10000100010010101.

%t Collatz[n_] := NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # > 1 &]; Table[FromDigits[Mod[Reverse[Collatz[n]], 2]], {n, 30}]

%Y Cf. A005186, A070165, A176999, A221467, A221468.

%K nonn,base

%O 1,2

%A _T. D. Noe_, Jan 17 2013