

A220145


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


4



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



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



KEYWORD

nonn,base


AUTHOR



STATUS

approved



