# Print all integers

Write a program or function which will provably print all integers exactly once given infinite time and memory.

Possible outputs could be:

0, 1, -1, 2, -2, 3, -3, 4, -4, …

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, -1, -2, -3, -4, -5, -6, -7, -8, -9, 10, 11, …


This is not a valid output, as this would never enumerate negative numbers:

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, …

• The output must be in decimal, unless your language does not support decimal integer (in that case use the natural representation of integers your language uses).

• Your program has to work up to the numbers with the biggest magnitude of the standard integer type of your language.

• Each integer must be separated from the next using any separator (a space, a comma, a linebreak, etc.) that is not a digit nor the negative sign of your language.

• The separator must not change at any point.

• The separator can consist of multiple characters, as long as none of them is a digit nor the negative sign (e.g. ,  is as valid as just ,).

• Any supported integer must eventually be printed after a finite amount of time.

### Scoring

This is , so the shortest answer in bytes wins

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• If our language supports infinite lists, can we output the list from a function rather than printing? (Calling print on such a list would print its elements one at a time forever.)
– xnor
Sep 16 '16 at 8:57
• I feel like the requirement on arbitrary-size integers does nothing but discourage languages without such integers from participating. They either have to have an import they can use or solve a totally different challenge from everyone else.
– xnor
Sep 16 '16 at 9:10
• @xnor Changed, though that kinds of ruins the very name of the challenge. Sep 16 '16 at 9:14
• @xnor, languages with arbitrary precision integers still have to solve a different problem from everyone else, so all that that change has accomplished is to make this problem boringly trivial in a lot of languages. Sep 16 '16 at 9:54
• @PeterTaylor Yeah, this is unfortunate. The wrapping solutions don't feel to me like they are printing any negatives, but I don't see a way to firmly specify the difference when it's a matter of representation.
– xnor
Sep 16 '16 at 9:58

# GolfScript, 11 bytes

0{.p.~p).}do

0            # push 0 to the stack
{           # this block will execute at least once, even though the TOS is 0
.p         # print the current number
.~p      # print the bitwise NOT of the current number
)     # increments the current number
.}do # creates an infinite loop


Because the bitwise NOT of x = (-x - 1), as the number increments, the inverse decrements. The bitwise NOT of 0 is -1, therefore it can be trivially proven that all integers are counted exactly once.

I know there's already a (longer) GolfScript solution here, I apologise if this is breaking any rules.

# AWK, 33 32 bytes

This code prints all integers in one line:

BEGIN{for(ORS=FS;;)print -i++,i}


An alternative 33-byte answer, which prints one integer per line:

BEGIN{for(;;)print n+=i++*(-1)^i}


Try it online!

# Pure yash and echo (or POSIX-compatible shell), 42 bytes

Separator is space or LF.

while echo ${#a}${a+-${#a}};do a=.$a;done


## How it works

• ${#a} is length of string contained in the variable. • ${a+xxx} is content of variable a, if a is null string; otherwise string xxx.
• Undefined variable is expanded to null string.

Try it online!

# JavaScript (Node.js), 38 bytes

for(n=-1;++n!=NaN;){console.log(n,-n)}


Try it online!

• When will 0 be printed? 2 days ago
• @thejonymyster fixed 2 days ago
• This prints 0 and -0. Does that count as posting each integer exactly once? :P 2 days ago
• @thejonymyster Yes, If you think 0 and -0 are the same. 2 days ago
• Well that's the problem, I do think that 0 and -0 are the same, and your program prints both of them. Zero twice, more than "exactly once" 2 days ago

# APL, 17 bytes

Pretty self explanatory

{∇⊃⎕←(⊢,-)1+⍵}⎕←0