Floating over the integers

Question

As you may know, the typical binary floating point numbers in a computer language are quite different than the typical integer numbers in a computer language. Floating point numbers can represent a much larger range, and can represent fractional amounts, however there is a trade-off that is frequently elided.

The distance between integers is constant, and in fact the value of that constant is one. The distance between floating point numbers, however, is variable, and increases the further one travels down the number line, away from the origin at 0. At some point, that distance is so large that the floating point numbers start skipping over integers, and many integers that are technically less than the maximum value of the floating point numbers, cannot actually be represented by floating point numbers.

The challenge:

Write a program that when given the number n, will print out the first n positive integers that cannot be represented by a floating point number in your language of choice.

• "First n positive integers" means, lowest in value, closest to the origin, and distinct from each other.

• Infinite precision floating point numbers are not allowed.

• It doesn't matter whether you choose 32 bit floats, 64 bits floats, or some other type of float, as long as it is a non-infinite precision floating point number in your language of choice, on your machine of choice.

• Order of numbers does not matter

• This is Code Gofl. Smallest number of characters wins.

• Good luck and have fun

Example:

In Rust, using 32 bit floating point builtin type 'f32':

n=4, result = [16777217,16777219,16777221,16777223]

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(updated - 1 order doesnt matter - 2 Golf->Gofl)

Answer 1

C (gcc), 58 bytes

f(n,i){for(i=9;n;i++)i-(int)(i+.0f)&&printf("%d ",i,n--);}

Try it online!

Works with 32-bit float.

Answer 2

Perl 6, 28 characters

{grep({.Num+|0-$_},^∞)[^$_]}

Try it online!

This is actually 30 bytes, but the challenge is scored in characters.

This should work theoretically. This creates a lazy list of numbers that compares the default number type (with arbitrary precision) against the same number converted to a Num datatype, which is a 64-bit floating point number, and returns the first \$n\$ elements of the list

Here's a version starting at \$2^{53}-5\$

Answer 3

Ruby 2.6, 42 bytes

->n{(1..).lazy.select{|i|i!=i*1.0}.take n}

Works with 64-bit floats, returns an enumerator.

Ruby 2.5 and below, 43 bytes

->n{1.step.lazy.select{|i|i!=i*1.0}.take n}

And finally, the one that actually finishes in reasonable time:

->n{(2**53).step.lazy.select{|i|i!=i*1.0}.take n}

Try it online!

Answer 4

Java 8, 68 67 bytes

n->{for(int i=9;;)if(++i!=(int)(i+0f))System.out.println(i*n/n--);}

Uses the 32-bit float, but by changing 0f to 0d and int to long it can also be tested with the 64-bit double.

Try it online with int and 0f.
Try it online with long and 0d.

Explanation:

n->{                       // Method with integer parameter and no return-type
  for(int i=9;;)           //  Loop `i` from 9 upwards indefinitely:
    if(++i                 //   Increase `i` by 1 first
          !=               //   And if it does not equal:
            (int)(i+0f))   //   Itself as float, and casted back to integer:
      System.out.println(i //    Print the current `i`
        *n/n--);}          //    And decrease `n` by 1
                           //    (and due to the `n/n`, the infinite loop will stop as soon
                           //     as `n` becomes 0, with a division by zero error)

Answer 5

JavaScript, 46 bytes

n=>{for(x=1n;n;)+[++x]!=x&&console.log(x)&n--}

This will certainly timeout on TIO. So, here is a TIO link which initialize x with 2⁵³.

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• Save 7 10 bytes, thanks to Neil.
• Save 2 bytes, thanks to Arnauld

Answer 6

cQuents, 9 bytes

&#N_=N+.0

Try it online!

& is broken on TIO right now, so TIO link will not work, but it would time out anyway, as the only way to start at 2^53 is modifing the interpreter.

Explanation

           Implicit input n
&          Output first n terms of the sequence
 #         Only include an integer N in the sequence if:
  N        N
   _=        is not equal to 
     N+.0                    N converted to float

Answer 7

Python 2, 57 bytes

n=1
exec"while n==int(.0+n):n+=1\nprint n;n+=1\n"*input()

Starting from 1 takes a very long time. For testing purposes, starting at \$2^{53}\$ gives the same results but much quicker: Try it online!

We count up values of n (an integer) until we find one for which converting to a float (by adding .0) and back to an int doesn't result in the same number. We then print that value and go to the next n. An exec loop lets us do this a fixed number of times according to the input.

Answer 8

C# (Visual C# Interactive Compiler), 54 bytes

n=>{for(int i=1;;)if(++i!=(int)(i+0f))Print(i*n/n--);}

Port of Kevin Cruijssen's Java answer

Try it online!

Answer 9

05AB1E (legacy), 10 bytes

µ¾ÐtnïÊi,¼

No TIO, because it will time out way before it reaches the first number 9007199254740993.. I'm using the legacy, since it is run in Python, so will output the same numbers as the Python answer. I'll see if I can determine the first few numbers for the new version of 05AB1E as well, which is run in Elixir (but that will be a separated answer in that case).

As alternative for the TIO, here a prove that tnï for input 9007199254740993 does not result in 9007199254740993, but in 9007199254740994 instead: Try it online.

Explanation:

µ           # Loop until the counter_variable is equal to the (implicit) input
            # (the counter_variable is 0 by default)
 ¾Ð         #  Push the counter_variable three times
   t        #  Take its square-root
    n       #  And then the square of that
     ï      #  And cast it back from a decimal to an integer
      Êi    #  If they are NOT equal:
        ,   #   Print the counter_variable
         ¼  #   And increase the counter_variable by 1

05AB1E has no builtin to set the counter_variable manually unfortunately, otherwise I would have set it to about 9007199254740000 at the start.