Generate an infinite group of infinite galaxies [closed]

Question

Here is the challenge as proposed by @trichoplax thanks to him for consolidating my post and standarizing it to PPCG common-rules.

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• A galaxy is a group of numbers where each one is mapped to another via a precise function f either a symbolic one or mathematical, a structure of numbers sharing some common points with this challenge i got inspired from with an exception that a galaxy sequence is not cyclic, but holds in a black hole, where more than one number can be mapped to it.
• A black hole is a specific unique number from a galaxy where all numbers (not individually) are mapped transitively to it, by repeating a function f infinitely over an infinite far number in a same galaxy, or just once if a number is the closest in the same galaxy, for example if the function is the ceiling of the square root then a black hole for the biggest galaxy so far excluding only the number 1 is 2, because mapping the closest number 3 or the infinite repetitively leads to the same number.

Task

Conceive a universe of an infinite number of distinct galaxies where all galaxies encompass an infinite number of integers.

Note that the example of ceiling of square root is banned for two reasons:

• The galaxy {1} is finite.
• There is a finite number of galaxies.

A valid example, is dividing by the smallest prime factor. This gives an infinite number of infinite galaxies.

2*2*3*5*5*7, 2*3*5*5*7, 3*5*5*7, 5*5*7, 5*7, 7, 7*5*5*5, 7*5*5*5....
5*5*7*11, 5*7*11, 11*7*7*7... , ....
...

Or one galaxy as a tree:

2*2*5 - 2*5 \
             \ 
2*3*5 - 3*5 - 5
3*3*5 /       |
             / 
2*5*5 - 5*5 /
3*5*5 /

Each galaxy consists of all numbers that share the same largest prime factor, and the function takes them all step by step towards the black hole which is that prime factor.

Note also, you may choose any domain of integers as long as the range is infinite, i mean you can exclude a range of numbers that makes the rest still boundless like {1,0} from last example.

Your program takes any integer input via a function's dimension , STDIN, and outputs an integer as the image mapped from this preimage, otherwise prints "error" or any string prespecified for an outputless range of enteries.

For the same example:

(IN/OUTPUT)

   20
   10


   15
   5


   77
   11


   0
   'undefined'


   1
   'undefined'

This is code-golf so shortest program in bytes wins.

I would have really liked to add a bonus-score for anyone who succeeds to find a function generating a universe without trees, alas, bonuses for code-golf are excluded.

Answer 1

Python 2, 15 bytes

lambda n:n>>n%2

The domain is nonnegative integers.

Answer 2

Python, 40 bytes

lambda n:n&~-n and int(bin(n)[3:],2)or n

Clear the top bit if there's more than one bit set, otherwise returns the number itself. The domain is the positive integers.

First couple numbers (in binary):

    1:     1
   10:    10
   11:     1
  100:   100
  101:     1
  110:    10
  111:    11
 1000:  1000
 1001:     1
 1010:    10
 1011:    11
 1100:   100
 1101:   101
 1110:   110
 1111:   111
10000: 10000
10001:     1
10010:    10
10011:    11
10100:   100
10101:   101
10110:   110
10111:   111
11000:  1000
11001:  1001
11010:  1010
11011:  1011
11100:  1100
11101:  1101
11110:  1110
11111:  1111

Answer 3

Pyth, 2 bytes

hP

Domain: integers ≥ 2. Function: smallest prime factor. Black holes: primes.

(This seems too simple but seems to satisfy the challenge as far as I can tell. Is the challenge missing some requirement? For example, perhaps the function is supposed to be surjective?)

Answer 4

Pyth, 5 4 bytes, no trees

I am working under the assumption that the author intended for the function to be surjective, and for “no trees” to mean that only black holes have multiple preimages. (Technically, a tree with only one branch is still a tree.)

ahxt

Domain: positive integers. Function: f(x) = |((x − 1) XOR x) + 1 − x|. Black holes: powers of 2. Galaxies:

1 ← 3 ← 5 ← 7 ← 9 ← 11 ← ⋯,
2 ← 6 ← 10 ← 14 ← 18 ← 22 ← ⋯,
4 ← 12 ← 20 ← 28 ← 36 ← 44 ← ⋯,
8 ← 24 ← 40 ← 56 ← 72 ← 88 ← ⋯,
⋮

Answer 5

Python 2, 29 bytes

lambda n:int("0"+`n`[1:])or n

Strips off the first digit, unless that makes the number 0. The domain is the positive integers.

Answer 6

05AB1E, 9 bytes

Code:

Dpiëf¬¹s/

Explanation:

Dpi         # if input is prime return input
   ë        # else
    f¬      # get the smallest primefactor
      ¹s/   # divide input by this factor

Domain:{n | n∈N ∧ n>1}

Range: {n | n∈N ∧ n>0}

Answer 7

JavaScript (ES6), 12 bytes

n=>n%2?n:n/2

The domain is the positive integers. The black holes are the odd numbers.

Answer 8

Pyth, 5 bytes

|stzz

Port of my Python answer (the decimal version).

Answer 9

matlab (156)

a=input('');if find(num2str(a)=='0')a,return,end,b=char(num2str(a)-1);c=str2num(b);if find(b=='0')if(find(num2str(c)=='0')&c)c,else 10^nnz(b)+c,end,else c,end

• I declare my self the winner of that imaginary score because i am the first who finds a universe of galaxies without trees.

• Domain is decimal numbers with two or more significant digits. and not a difference bteween two arbitray digits squals to 9 .

• Black holes are numbers which have significant zeros, either in the extreme bottom, or between two strictly positive digits 12300131 , 123400 , 10 , ....

• The function is decrementing all decimal digits of that number by 1, if we stumble upon a significant zero we declare a blackhole, if non-significant zero at the head of this number, precede it with 1 then the result topped by unsignificant zeos.

• There is no trees in that galaxy except the blackhole which absorbs an infinite tree-less streams of finite numbers.