# Smallest palindrome divisible by the input

Given a positive integer N, output the smallest positive integer such that this number is a palindrome (i.e. is its own reverse) and is divisible by N.

The palindrome (i.e. the output) must not need a leading zero to be a palindrome, e.g. 080 is not the valid answer for 16.

The input will never be a multiple of 10, because of the previous reason.

Your program may take as much time as necessary, even if in practice it would be way too long to output the answer.

### Inputs and outputs

• You may take the input through STDIN, as a function argument, or anything similar.
• You may print the output to STDOUT, return it from a function, or anything similar.
• Inputs and outputs must be in the decimal base.

### Test cases

N        Output
1        1
2        2
16       272
17       272
42       252
111      111
302      87278
1234     28382


### Scoring

This is , so the shortest answer in bytes wins.

• Will the input be divisible by 10? – Leaky Nun Aug 25 '16 at 7:01
• @LeakyNun No, because then there is no solution since the palindrome must not need a leading zero. I will make that explicit. – Fatalize Aug 25 '16 at 7:04
• Will the input be positive? – Wheat Wizard Aug 25 '16 at 14:01
• @WheatWizard Yes: Given a positive integer N – Fatalize Aug 25 '16 at 14:29
• @Fatalize sorry. I don't know how I missed it. – Wheat Wizard Aug 25 '16 at 14:38

# 2sable / 05AB1E, 6 / 7 bytes

2sable

[DÂQ#+


Explanation

[         # infinite loop
D        # duplicate current number
Â       # bifurcate
Q#     # if the number is equal to its reverse, break loop
# implicitly print


Try it online

05AB1E

[DÂQ#¹+


The difference to the 2sable code is that input is only implicit once in 05AB1E, so here we need ¹ to get the first input again.

Try it online

Saved 1 byte with 2sable as suggested by Adnan

• @Fatalize I was just writing it up :) – Emigna Aug 25 '16 at 6:57
• If you switch to 2sable, you can save a byte by doing this: [DÂQ#+. – Adnan Aug 25 '16 at 8:42
• @Adnan: Right! The repeated implicit input saves a byte :) – Emigna Aug 25 '16 at 8:46

(+)>>=until((reverse>>=(==)).show)


# Pyth, 7 bytes

*f_I*Q


Try it online: Demonstration

### Explanation

*f_I*QT)Q   implicit endings, Q=input number
f      )    find the first number T >= 1, which satisfies:
*QT        product of Q and T
           as string
_I            is invariant under inversion (=palindrom)
*        Q   multiply this number with Q and print

• After reading so many codegold questions I'm starting to think that Pyth will be next JS/Java/Ruby/Python... – agilob Aug 25 '16 at 12:00
• @agilob oh dear god pls no. – Alexander Aug 26 '16 at 20:14

# Java, 164 159 126 108 94 bytes

Golfed version:

int c(int a){int x=a;while(!(x+"").equals(new StringBuffer(x+"").reverse()+""))x+=a;return x;}


Ungolfed version:

int c(int a)
{
int x = a;
while (!(x + "").equals(new StringBuffer(x + "").reverse() + ""))
x += a;
return x;
}


Shoutout to Emigna and Kevin Cruijssen for contributing improvements and cutting the bytes almost in half :)

• Isn't x % a == 0 kind of redundant when you initialize x as a and only increase it by a? Also, can the comparison with the reversal of the string be done in the while conditional? – Emigna Aug 25 '16 at 9:12
• You can remove import org.apache.commons.lang.StringUtils; and use org.apache.commons.lang.StringUtils.reverse directly. for(;;) is shorter than while(1>0). No need for a full program, just int c(int a){...} would do as a valid answer, since the question has the following rule: "You may take the input as a function argument. You may return the output from a function." @Emigna is indeed right that the modulo check isn't necessary. – Kevin Cruijssen Aug 25 '16 at 9:18
• Oh, and welcome of course! You might like this post: Tips for golfing in Java. – Kevin Cruijssen Aug 25 '16 at 9:19
• @Emigna: you're absolutely right, did that. – peech Aug 25 '16 at 9:23
• @KevinCruijssen: since I only iterate through numbers which are divisible by a (by x += a). I don't have to check for divisibility :) and thanks for the golfing tips! – peech Aug 25 '16 at 9:25

C#, 103 80 Bytes

int f(int p){int x=p;while(x+""!=string.Concat((x+"").Reverse()))x+=p;return x;}


Ungolfed

int f(int p)
{
int x = p;
while (x + "" != string.Concat((x + "").Reverse()))
x += p;
return x;
}

• You might save some bytes by removing i, and incrementing via x+=p. – stannius Aug 25 '16 at 15:59
• replacing x.ToString() with 'x+"" will save a bunch of chars. – user8865 Aug 25 '16 at 22:07

# Python 2, 46 bytes

f=lambda x,c=0:c[::-1]==cand c or f(x,c+x)


Ideone it!

Recursive solution with c as counter.

The case for 0 is interesting, because although c=0 satisfies the palindrome condition, it would not be returned, because ccc and 0 or xxx always returns xxx.

• It's a bit shorter to do c*(c[::-1]==c)or. – xnor Aug 25 '16 at 18:34

# PHP, 39 bytes

while(strrev($i+=$argv[1])!=$i);echo$i;

• Takes number N as argument $argv[1]; • ; after while to do nothing • strrev return string backward Same length with for-loop for(;strrev($i+=$argv[1])!=$i;);echo$i;  # Brachylog, 8 bytes :L#>*.r=  Try it online! (around 5 seconds for 1234) Verify all testcases. (around 20 seconds) :L#>*.r= ?:L#>*.r=. Implicitly filling Input and Output: Input is prepended to every predicate, Output is appended to every predicate. ?:L *. Input*L is Output, L#> L is positive, .r . Output reversed is Output, =. Assign a value to Output.  # Javascript (ES6), 55 51 bytes 4 bytes thanks to Neil. f=(x,c=x)=>c==[...c+""].reverse().join?c:f(x,x+c) <input type=number min=1 oninput=o.textContent=this.value%10&&f(+this.value)><pre id=o> • From playing around while creating your code snippet for you, the first + seems unnecessary. – Neil Aug 25 '16 at 9:51 • Would (x,c=x) allow you to avoid the &&c? – Neil Aug 25 '16 at 9:51 • I think you can do c^[...c+""].reverse().join?f(x,x+c):c to save one more byte. – Arnauld Aug 25 '16 at 17:54 • c- would work for slightly higher numbers than c^, if necessary. – Neil Aug 25 '16 at 19:11 ## Pyke, 11 9 bytes .f*D_q)*  Try it here! # C, 217 189 bytes Standalone version : int a(char*b){int c=strlen(b);for(int i=0;i<c/2;i++)if(b[i]!=b[c-i-1])return 0;}int main(int e,char **f){int b,c;char d[9];b=atoi(f[1]);c=b;while(1){sprintf(d,"%d",c);if(a(d)&&(c/b)*b==c)return printf("%d",c);c++;}}  Call to a function version : int s(char*a){int b=strlen(a);for(int i=0;i<b/2;i++)if(a[i]!=a[b-i-1])return 0;}int f(int a){int b;char c[9];b=a;while(1){sprintf(c,"%d",b);if(s(c)&&(b/a)*a==b)return printf("%d",b);b++;}}  Ungolfed : #include <stdlib.h> #include <string.h> #include <stdio.h> int check_palindrome(char *str) { int length = strlen(str); for (int i = 0; i < length / 2; i++) { if (str[i] != str[length - i - 1]) return 0; } return 1; } int main(int argc, char **argv) { int number; int pal; char string[15]; number = atoi(argv[1]); pal = number; while (1) { sprintf(string, "%d", pal); if (check_palindrome(string) && (pal / number) * number == pal) { printf("%d\n", pal); return 1; } pal++; } return 0; }  Call to a function ungolfed : int s(char *a) { int b = strlen(a); for (int i = 0; i < b / 2; i++) { if (a[i] != a[b - i - 1]) return 0; } return 1; //We can remove it, it leads to a undefined behaviour but it works } int f(int a) { int b; char c[9]; b = a; while (1) { sprintf(c, "%d", b); if (s(c) && (b / a) * a == b) { printf("%d\n", b); //no need for the \n return 1; //just return whatever printf returns, who cares anyway ? } b++; } return 0; //no need for that }  I included the standalone version for historicity. This is my first codegolf, any comment is welcome ! • I recommend making a separate function for the challenge, and not counting main() regardless of your preferences. You wouldn't play baseball by running twelve loops around first before tagging "because I prefer it," you will never reach safely. This is a competition, and the primary rule is to use any means necessary and legal to reduce byte count. – user18932 Aug 25 '16 at 17:46 • @Snowman fair enouth, I edited my answer to include a 'call to a function' version. This allows me to take an int as parameter and gold away a few more bytes. – Valentin Mariette Aug 26 '16 at 9:11 • do your function compile without "include <string.h>"? if the answer is not than i can use #define F for or #define R return without make it in count... – user58988 Aug 28 '16 at 8:53 • @RosLuP yeah, I get a few warnings but gcc is able to compile it. – Valentin Mariette Aug 30 '16 at 9:56 • Hi!, I would like drop some Hints! 1) C has implicit int so you can change the code like this int f(int a) -> f(a) 2) if you have to declare some ints you can use the function parameters: int f(int a){int b; -> f(a,b){ 3) sprintf will never return 0 so you ca use in the while: while(1){sprintf(c,"%d",b); -> while(sprintf(c,"%d",b)){ 4) use the K&R C for define a Function so tou can combo with my 2nd hint: int s(char*a){int b=strlen(a);for(int i=0 -> s(a,b,i)char*a;{b=strlen(a);for(i=0; – Giacomo Garabello Jan 4 '17 at 17:41 # R, 117113109 101 bytes D=charToRaw;P=paste;S=strtoi;a=P(i<-scan()+1);while(!all(D(a)==rev(D(a))&&S(a)%%i==0)){a=P(S(a)+1)};a  Ungolfed i<-scan() #Takes the input D=charToRaw #Some aliases P=paste S=strtoi a=P(i+1) #Initializes the output while(!(all(D(a)==rev(D(a)))&&(S(a)%%i==0))) #While the output isn't a palindrom and isn't #divisible by the output... a=P(S(a)+1) a  all(charToRaw(a)==rev(charToRaw(a))) checks if at each position of a the value of a and its reverse are the same (i.e., if a is palindromic). It might be possible to golf out some bytes by messing around with the types. # Actually, 15 14 bytes Asked to answer by Leaky Nun. Golfing suggestions welcome. Try it online! ╖2╜*$;R=╓N╜*


Ungolfing

          Implicit input n.
╖         Save n in register 0.
2...╓   Push first 2 values where f(x) is truthy, starting with f(0).
╜*$Push register 0, multiply by x, and str(). ;R Duplicate str(n*x) and reverse. = Check if str(n*x) == reverse(str(n*x)). The map will always result in [0, the x we want]. N Grab the last (second) value of the resulting list. ╜* Push n and multiply x by n again. Implicit return.  # Haskell, 64 63 56 bytes x!n|mod x n==0,s<-show x,reverse s==s=x|y<-x+1=y!n (1!)  Call with (1!)16 or simply 1!16. Try it on Ideone. VBSCRIPT, 47 bytes do:i=i+1:a=n*i:loop until a=eval(strreverse(a))  ungolfed do #starts the loop i=i+1 #increments i, we do it first to start at 1 instead of 0 a= #a is the output n*i #multiply our input n by i loop until a=eval(strreverse(a)) #end the loop when our output is equal to its reverse  # Perl, 25 bytes Includes +2 for -ap Run with the input on STDIN: palidiv.pl <<< 16  palidiv.pl: #!/usr/bin/perl -ap$_+="@F"while$_-reverse  # S.I.L.O.S, 109 bytes readIO n = 0 lbla n + i a = n r = 0 lblb m = a m % 10 r * 10 r + m a / 10 if a b r - n r | if r a printInt n  Try it online! # Japt, 14 bytes V±U s w ¥V?V:ß  Try it online! Thank you ETHproductions for the help! :) # MATL, 10 bytes 0G+tVtP<a  Try it online! 0 % Push 0  % Do...while G+ % Add the input. This generates the next multiple of the input tV % Duplicate, convert to string tP % Duplicate, reverse <a % Is any digit lower than the one in the reverse string? This is the % loop condition: if true, the loop proceeds with the next iteration % End do...while % Implicitly display  ## PowerShell v2+, 72 bytes for($i=$n=$args[0];;$i+=$n){if($i-eq-join"$i"["$i".Length..0]){$i;exit}}


Long because of how reversing is handled in PowerShell -- not very well. ;-)

Takes input $args[0], stores into $i (our loop variable) and $n (our input). Loops infinitely, incrementing $i by $n each time (to guarantee divisibility). Each iteration, we check whether $i is a palindrome. There's some trickery happening here, so let me explain. We first take $i and stringify it with "$i". That's then array-indexed in reverse order ["$i".length..0] before being -joined back into a string. That's fed into the right-hand side of the -equality operator, which implicitly casts the string back into an [int], since that's the left-hand operand. Note: this casting does strip any leading zeros from the palindrome, but since we're guaranteed the input isn't divisible by 10, that's OK. Then, if it is a palindrome, we simply place $i onto the pipeline and exit. Output is implicit at the end of execution.

### Test Cases

PS C:\Tools\Scripts\golfing> 1,2,16,17,42,111,302,1234|%{"$_ -> "+(.\smallest-palindrome-divisible-by-input.ps1$_)}
1 -> 1
2 -> 2
16 -> 272
17 -> 272
42 -> 252
111 -> 111
302 -> 87278
1234 -> 28382


# MATLAB, 76 bytes

function s=p(n)
f=1;s='01';while(any(s~=fliplr(s))) s=num2str(n*f);f=f+1;end


Call format is p(302) result is a string.

Nothing clever here. It does a linear search, using the num2str() and fliplr() functions.

This ugly arrangement is a touch shorter than using a while(1) ... if ... break end pattern.

Ungolfed

function s = findFirstPalindromeFactor(n)
f = 1;                        % factor
s = '01';                     % non-palindromic string for first try
while( all(s ~= fliplr(s)) )  % test s not palindrome
s = num2str( n * f );       % factor of input as string
f = f + 1;                  % next factor
end



## Mathematica, 49 bytes

(c=#;Not[PalindromeQ@c&&c~Mod~#==0]~While~c++;c)&


Starts the search at c = N, and increments c if not a palindrome and not divisible by N. When conditions are met, outputs c.

# Jelly, 12 bytes

¹µ+³ßµDU⁼Dµ?


Try it online!

Explanation:

This link takes 1 argument. The µs split it into 4 parts. Starting from the last and moving left:

           ? The three parts in front of this are the if, else, and
condition of a ternary expression.
DU⁼D  This condition takes a number n as an argument. It converts
n to an array of decimal digits, reverses that array, and
then compares the reversed array to the decimalization of
n (ie is n palindromic in decimal?)
+³ß  This is the else. It adds the original input argument to n
and then repeats the link with the new value of n.
¹  This is the if. It returns the value passed to it.


# Elixir, 75 bytes

def f(p,a\\0),do: if'#{a+p}'|>Enum.reverse=='#{a+p}',do: a+p,else: f(p,a+p)


## Python 2, 66 65 bytes

i is input and x is (eventually) output

def f(i,x):
y=x if x%i==0&&x==x[::-1]else f(i,x+1)
return y


After scrolling through other answers I found a shorter Python 2 answer but I put the effort into my solution so might as well throw it here. ¯\_(ツ)_/¯

• You can remove the space in [::-1] else. – mbomb007 Aug 26 '16 at 19:41
• can't you remove the assignment of y, and just put the expression on the end of the return? return x if x%i==0&&x==x[::-1]else f(i,x+1), which then means you can make it a lambda, and golf more bytes? – Destructible Lemon Sep 24 '16 at 3:01

# REXX, 46 bytes

arg a
do n=a by a until reverse(n)=n
end
say n


# Python 2, 44 bytes

x=lambda n,m=0:m*(m==m[::-1])or x(n,m+n)


Try it online!

I know that the question was posted over six months ago, but this was shorter than any other Python submission.

## QBIC, 29 bytes

:{c=a*q~!c$=_f!c$||_Xc\q=q+1


Explanation:

:      Get cmd line param as number 'a'
{      DO
c=a*q  multiply 'a' by 'q' (which is 1 at the start of a QBIC program) and assign to 'c'
~      IF
!c$'c' cast to string = equals _f!c$| 'c' cast to string, the reversed
|      THEN
_Xc    Quit, printing 'c'
\q=q+1 ELSE increment q and rerun
DO Loop is auto-closed by QBIC, as is the IF


# Perl 6, 35 bytes

->\N{first {$_%%N&&$_==.flip},N..*}

->\N{first {$_==.flip},(N,N*2...*)}  ->\N{(N,N*2...*).first:{$_==.flip}}


## Explanation:

-> \N {
# from a list of all multiples of the input
# ( deduced sequence )
( N, N * 2 ... * )

# find the first
.first:

# that is a palindrome
{ $_ == .flip } }  ## Perl 6, 39 bytes my &f={first {.flip==$_},($_,2*$_...*)}


(33 not including the my &f=`)