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Your task is to generate the nth term of the RATS sequence, where n is the input. The RATS sequence is also known as the Reverse Add Then Sort sequence. This sequence can also be found here:

test cases:

0 > 1
1 > 2
2 > 4
3 > 8
4 > 16
5 > 77
6 > 145
7 > 668

For example, the output for 5 is 77 because 16 + 61 = 77. After this the 77 is sorted.

Shortest submission wins. This is my first challenge so i hope this is not a duplicate or something.

share|improve this question
Does the input have to be an Integer or could it also be a string? – DenkerAffe Jan 31 at 15:36
@DenkerAffe do you mean a number in the form of a string? – justaprogrammer Jan 31 at 15:37
@justaprogrammer Yea, so I can get "123" instead of 123 as Integer. Would mayve save some bytes. – DenkerAffe Jan 31 at 15:40
isn't 77+77=154? Or have I missed something? EDIT: Oh, yes, I forgot to sort. – Denham Coote Feb 1 at 10:48
@DenhamCoote I think you meant "oh rats, I forgot to sort!" – Martin Ender Feb 2 at 10:49

18 Answers 18

MATL, 11 12 bytes


Input is a string (with single quotes) representing an integer in unary. String input is allowed by the challenge, and unary is a valid format.

Try it online!


1      % push number 1 to the stack
i      % input. Will be a string of "n" ones 
"      % for loop: repeat n times (consumes string)
  t    %   duplicate
  V    %   convert to string
  P    %   reverse
  U    %   convert to number
  +    %   add
  V    %   convert to string
  S    %   sort
  U    %   convert to number
       % loop is implicitly ended
       % stack content is implicitly displayed    
share|improve this answer
I don't know which scares/perplexes me more, MATL or Jelly... +1 – Downgoat Jan 31 at 19:00

CJam, 15 bytes


Test it here.


1     e# Push 1 as the start of the sequence.
ri    e# Read input and convert to integer N.
{     e# Run this block N times...
  _s  e#   Duplicate and convert to string.
  W%  e#   Reverse string.
  i+  e#   Convert back to integer and add to previous value.
  s$  e#   Convert to string and sort.
  i   e#   Convert back to integer for the next iteration.
share|improve this answer
how can all these languages be so short – justaprogrammer Jan 31 at 15:52
@justaprogrammer Single-character names for built-in functions help. ;) CJam, Pyth and Brachylog are all golfing languages, specifically designed with code golf in mind. (See Then there's also languages like APL and J that aren't golfing languages at all but are similarly terse, because the designers thought it would be a good idea. – Martin Ender Jan 31 at 15:54
Which one do you recommend the most for winning challenges like these? – justaprogrammer Jan 31 at 16:03
@justaprogrammer I wouldn't pick one based on which one is winning these challenges (that would likely be Pyth or Jelly). It can be just as fun to golf in a "normal" language (especially because there might be more competition within that language). For a golfing language, it's probably more important that you enjoy using it. CJam is quite fun - it's a stack-based which makes you bend your mind a bit more than other languages, and at the same time it's quite a powerful language, that I've started to use for simple throwaway scripts outside of golf, which is a good boost to my productivity. – Martin Ender Jan 31 at 16:07
These languages look very interesting and I can't wait to learn one myself. I don't know what jelly is? Is that some kind of gelatine or something? – justaprogrammer Jan 31 at 16:23

Pyth, 17 13 12 bytes

u        Q\1    reduce range(input()) on base case of "1" (string)
   +vG          eval the string (to get a number), and add...
      v_G       the same number, reversed first and then eval'd
 S`             convert back to string and sort

Try it on the online interpreter.

share|improve this answer
What is this magic? How does this work? – justaprogrammer Jan 31 at 15:42
@justaprogrammer I've added an explanation. :) – Doorknob Jan 31 at 16:00
Huh, but how. How do you test this code? – justaprogrammer Jan 31 at 16:02
@justaprogrammer I've added a link to an online interpreter that you can run the code on. – Doorknob Jan 31 at 16:06
This is awesome, it is so short, yet so beautiful – justaprogrammer Jan 31 at 16:11

05AB1E, 6 bytes




$       # Push 1 and input
 F      # For N in range(0, input)
  D     # Duplicate top of the stack
   R    # Reverse top of the stack
    +   # Add top two items
     {  # Sort top of the stack
        # Implicitly print top of the stack

This also works with a 0 byte program.

share|improve this answer
@Adnan Three days ago, actually. Still, well played... – Doorknob Jan 31 at 19:23
@Doorknob Just in time haha – Adnan Jan 31 at 19:28
You can save 6 bytes by eliminating your source code. – Dennis Jan 31 at 21:00
You can also shorten 05AB1E by first eliminating the leading zero, and then omitting the 1, as 1E==E. Then you get just 5ABE, -2 bytes. – flawr Jan 31 at 23:49
@Dennis great observation – Adnan Feb 1 at 20:48

Python 2, 72

f=lambda x,n=1:x and f(x-1,int(''.join(sorted(`n+int(`n`[::-1])`))))or n

Recursive function, makes use of the Python 2 shorthand for __repr__, which will break once the function reaches very large values (an L will be appended to the number's string), I'm not certain from the spec if there is a place where we can stop, but if not changing to str() only adds 6 bytes, but then it becomes slightly shorter to output as a string, at 75 bytes:

f=lambda x,n='1':x and f(x-1,''.join(sorted(str(int(n)+int(n[::-1])))))or n

1 byte saved thanks to trichoplax on this version

share|improve this answer
Is that a surplus space before the or in the second code block? – trichoplax Feb 1 at 2:09
@trichoplax thanks for the catch :) – FryAmTheEggman Feb 1 at 2:21

JavaScript ES6, 70 bytes

Saved 1 byte thanks to @user81655


sigh JavaScript is really verbose. A lot (> 50%) of the code is just case to string + array function + join + cast to int. I've tried reduce, eval, and all sorts of stuff but this seems to be the shortest.

Try it online (All browsers work)

share|improve this answer
Just like mine, but better (and posted earlier). Bah! – edc65 Jan 31 at 16:04
String Manipulation is JS is so long, you have my condolences – MayorMonty Jan 31 at 18:24
@user81655 cool, thanks! I would of never thought to re-order that way – Downgoat Feb 1 at 3:17

Brachylog, 19 bytes

0,1 .|-1=:0&Rr+R=o.


0,1 .               § If Input is 0, unify the Output with 1
     |              § Else
      -1=:0&R       § unify R with the output of this main predicate, with input = Input - 1
             r+R=o. § Reverse R, add it to itself and order it, then unify with the Output.
share|improve this answer

Haskell, 67 bytes

import Data.List
g i=i:g(sort$show$read i+read(reverse i))

Usage example: (g"1"!!) 7-> "668".

It's a direct implementation of the definition: starting with "1", repeatedly append the reverse-add-sort result of the current element. The main function (g"1"!!) picks the ith element.

share|improve this answer
This is the most readable program under 70 bytes! – Gaurav Agarwal Feb 1 at 23:54

Julia, 77 bytes

n->(x=1;for _=1:n x=(p=parse)(join(sort(["$(x+p(reverse("$x")))"...])))end;x)

This is a lambda function that accepts an integer and returns an integer. To call it, assign it to a variable.


function f(n::Int)
    # Begin x at 1
    x = 1

    # Repeat this process n times
    for _ = 1:n
        # Add x to itself with reversed digits
        s = x + parse(reverse("$x"))

        # Refine x as this number with the digits sorted
        x = parse(join(sort(["$s"...])))

    # Return x after the process (will be 1 if n was 0)
    return x
share|improve this answer

Jelly, 13 12 bytes

I'm sure this can probably be golfed, as this is my first answer in Jelly/in a tacit language.

DUḌ+ðDṢḌ Performs RATS
1Ç¡      Loops

D        Converts integer to decimal
 U       Reverses
  Ḍ      Converts back to integer
   +     Adds original and reversed
    ð    Starts new chain
     D   Converts back to decimal
      Ṣ  Sorts
       Ḍ Back to integer again

1        Uses 1 instead of input
 Ḍ       Uses line above
  ¡      For loop

EDIT: Saved 1 byte, thanks to Dennis

share|improve this answer

Lua, 179 Bytes

I can't see how I could golf it more, but I'm sure there's a way.

tonumber is used again and again because I have to convert a to a string to reverse it, do the addition, and go back to a string to sort it.

a,z=0,table for i=0,tonumber( t={}(""..a+tonumber((""..a):reverse())):gsub(".",function(d)z.insert(t,d)end)z.sort(t)a=a<1 and 1 or tonumber(z.concat(t,""))end print(a)

Ungolfed and explanations

z=table                              -- z is a pointer on the table named table
                                     -- it allows me to use its functions
                                     -- while saving 4 bytes/use

for i=0,tonumber(          -- Iterate n times for the nth element
  (""..a+tonumber((""..a):reverse()))-- we add a with its "reversed" value
                                     -- and convert the whole thing to a string
    :gsub(".",function(d)            -- for each character in it, use an anonymous fucntion
       z.insert(t,d)end)             -- which insert them in the array t
  a=a<1 and 1 or                     -- if i==0, a=1
     tonumber(z.concat(t,""))        -- else we concat t in a string and convert it to number
share|improve this answer

Java 1.8, 251 bytes

interface R{static void main(String[]a){int i,r,n=1,c=0,t=Byte.valueOf(a[0]);while(++c<=t){i=n;for(r=0;i!=0;i/=10){r=r*10+i%10;}n+=r;a[0]=n+"";char[]f=a[0].toCharArray();java.util.Arrays.sort(f);n=Integer.valueOf(new String(f));}System.out.print(n);}}


interface R{
static void main(String[]args){
    int input,reversed,nextValue=1,count=0,target=Byte.valueOf(args[0]);
        nextValue=Integer.valueOf(new String(sortMe));
share|improve this answer
Why do you use interface R instead of class R which is 4 bytes shorter? – Will Sherwood Feb 2 at 5:04
@WillSherwood because you can then omit the public modifier on main(), making it shorter overall :) – Denham Coote Feb 2 at 8:08

ES6, 79 bytes


82 bytes without eval:


All those conversions are painful.

@edc65 I actually saved 4 bytes by switching from map to reduce this time... no doubt you'll prove me wrong again though.

share|improve this answer
for is shorter: n=>eval("for(r=1;n--)r=+[...+[...r+''].reverse().join``+r+''].sort().join``‌​") – Downgoat Jan 31 at 16:01
@Doᴡɴɢᴏᴀᴛ Doesn't work for n=0, even after I've fixed the syntax errors. – Neil Jan 31 at 16:03

Python 2, 91 Bytes

Input as Integer, result is printed to the screen.

def f(n):
 for i in range(n):t=int("".join(sorted(str(int(str(t)[::-1])+t))))
 print t

This could be a lot shorter with some recursion magic I guess, but I cant wrap my head around it yet. Gonna have a fresh look later and hopefully improve this one.

share|improve this answer

Python 2, 83 bytes

def f(n):
 for _ in v*n:v=''.join(sorted(str(int(v)+int(v[::-1]))))
 print v
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Perl 6, 40 bytes

{(1,{[~] ($_+.flip).comb.sort}...*)[$_]} # 40

( If you want it to return an Int put a + right before [~] )


# give it a lexical name
my &RATS = {…}

say RATS 5; # 77

# This implementation also accepts a list of indexes

# the first 10 of the sequence
say RATS ^10; # (1 2 4 8 16 77 145 668 1345 6677)
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Mathematica 10.3, 66 61 bytes


Quite simple.

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Seriously, 17 bytes


Try it online!


1              push 1
 ,`       `n   do the following n times:
   ;$R≈        reverse
       +       add
        $S≈    sort
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