A220145 The Collatz (3x+1) iteration mod 2 with bits combined.

1, 10, 10000101, 100, 100001, 100001010, 10000100010010101, 1000, 10000100010010101001, 1000010, 100001000100101, 1000010100, 1000010001, 100001000100101010, 100001000001010101, 10000, 1000010001001, 100001000100101010010, 100001000100101000101, 10000100

Offset

1,2

Comments

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

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.

Links

T. D. Noe, Table of n, a(n) for n = 1..10000

Example

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.

Mathematica

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

Crossrefs

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

Sequence in context: A013854 A210813 A116126 * A057141 A034249 A358815

Adjacent sequences: A220142 A220143 A220144 * A220146 A220147 A220148

Keyword

nonn,base

Author

T. D. Noe, Jan 17 2013

Status

approved