# Find the closest palindromic number

Given a number N, output/return X so that N+X is a palindrome, where |X| has to be as small as possible.

Palindrome: A number is a palindrome, if its sequence of digits is the same when reading them from left to right as when reading from right to left.
95359 and 6548456 are symmetric, 123 and 2424 are not. Numbers with leading zeros such as 020 are not a palindrome.

Input is a positive integer smaller than 1015. Read it from stdin, as a method-parameter, whatever.

Output has to be an integer (positive or negative) and ought to be 0 if the input is already a palindrom. You may write your output to stdout, return it from a function or whatever you like. If there are 2 numbers (e.g. 2 and -2) that satisfy the requirements, output only one of them.

Examples:

Input             Output
3                 0
234               -2
1299931           -10
126               5 or -5 (only one of them)

• Presumably if a number is halfway between the two nearest palindromes, either is an acceptable output? E.g. for N=10 the output can be X=-1 or X=1? – Peter Taylor Aug 27 '14 at 13:45
• @PeterTaylor Yes, it just has to be as small as possible. – CommonGuy Aug 27 '14 at 13:47

# Pyth, 26 20

Lnb_bWP+QZ=Z-g0ZZ)Z


Updated to meet the new rules.

The program runs in an infinite loop which tests every possible increment, in the order 0, -1, 1, -2, -2 ...

Explanation:

Q=eval(input())     implicit
Z=0                 implicit
Lnb_b               def P(b): return b != rev(b)
WP+QZ              while P(repr(Q+Z)):
=Z-g0ZZ             Z=(0>=Z)-Z
)                   <end while>
Z                   print(Z)


Example run:

python3 pyth.py programs/palin.pyth <<< 965376457643450
-2969881


This took 23 seconds.

Bonus solution, same character count:

Wn+QZ_+QZ=Z-g0ZZ)Z

• Just to let you know, the rules changed to finding the nearest palindrome (in either direction). But I guess since you posted before that rule change there's no obligation for you to fix it. – Martin Ender Aug 27 '14 at 14:12
• Might it save chars to loop Z through [0, 1, -1, 2, -2, ...] by an update Z=-Z+(Z<0)? – xnor Aug 27 '14 at 20:37
• Yep - I thought of that independently. – isaacg Aug 27 '14 at 23:31
• @xnor Added. Filler. – isaacg Aug 27 '14 at 23:36
• Ok, cool. Have you also looked into putting the negation of the condition into the while? And maybe saving a repr by applying it to the input to P? – xnor Aug 27 '14 at 23:40

# Ruby, 111 84 bytes

i=$*[j=-1].to_i r=->j{s=(i+j).to_s abort(j.to_s)if s==s.reverse} loop{r[j+=1] r[-j]}  Takes the number as its only command-line argument. • How about this website? – CommonGuy Aug 27 '14 at 13:59 • @Manu Thanks didn't know that one! My submission works as far as I can tell. – Martin Ender Aug 27 '14 at 14:01 # CJam, 3429 25 bytes q~:I!{:R1<R-RI+_W%=!}g;R  Try it online. ### Examples $ cjam palfind.cjam <<< 120; echo
1
$cjam palfind.cjam <<< 121; echo 0$ cjam palfind.cjam <<< 122; echo
-1


### How it works

q~:I    " Read from STDIN, evaluate and save the result in “I”.                           ";
!       " Compute the logical NOT (0 since the integer is positive).                      ";
{       "                                                                                 ";
:R    " Save the topmost integer in “R”.                                                ";
1<R-  " Compute (R < 1) - R. This produces the sequence 0 → 1 → -1 → 2 → -2 → … .       ";
RI+   " Push I + R.                                                                     ";
_    " Cast to string and push a copy.                                                 ";
W%=!  " Check if the reversed copy matches the original.                                ";
}g      " If it doesn't, repeat the loop.                                                 ";
;R      " Discard the integer on the stack and push “R”.                                  ";


f n=[x-n|x<-[0..]>>= \v->[n+v,n-v],show x==(reverse.show)x]!!0


Save it to a file named golf.hs and then test it with ghci:

*Main> :l golf
[1 of 1] Compiling Main             ( golf.hs, interpreted )
*Main> map f [1000..1050]
[-1,0,-1,-2,-3,-4,-5,-6,-7,-8,-9,-10,-11,-12,-13,-14,-15,-16,-17,-18,-19,-20,-21,-22,-23,-24,-25,-26,-27,-28,-29,-30,-31,-32,-33,-34,-35,-36,-37,-38,-39,-40,-41,-42,-43,-44,-45,-46,-47,-48,-49]
*Main>

• how about writing x<-[0..]>>=(\v->[n+v,n-v]) ? It is shorter and it makes it a one-liner – proud haskeller Aug 28 '14 at 7:43
• @proudhaskeller Thanks! Very elegant trick with the list monad. – Ray Aug 28 '14 at 7:50

# Python 2.7, 98, 81

Creates a palindrome from the input number, then subtracts that from the input to find the delta.

def f(n):
m=map(int,str(n));l=len(m)/2;m[-l:]=m[l-1::-1];return int(m[1::3])-n


usage:

print f(3)          # 0
print f(234)        # -2
print f(2342)       # -10
print f(129931)     # -10
print f(100000)     # 1


ungolfed and annotated:

def f(n):                      # take a integer n
m=map(int,str(n));         # convert n into array of ints
l=len(m)/2;                # get half the length of the array of ints
m[-l:]=m[l-1::-1];         # replace the last elements with the first elements reversed
return int(m[1::3])-n    # convert array of ints backinto single int and subtract the original number to find the delta

• This doesn't give the smallest delta. f(19) = -8 (palindrome 11), where it should be +3 to make 22. – Geobits Aug 27 '14 at 18:31
• @Geobits Yes, the 10-100 values will give me a problem with this approach – Moop Aug 27 '14 at 18:47
• It's not just those. Similarly, 199999 gives -8 instead of 3, 9911 gives 88 instead of -22. Just reversing the first digits doesn't work to get the smallest delta in a lot of cases. – Geobits Aug 27 '14 at 18:52
• well i wouldn't say a lot of cases, i bet 99.9% of cases it works for. But yes, it needs to work for 100% of cases – Moop Aug 27 '14 at 18:55
• @Geobits. Sure, so 27% error rate there. But when you get to the 100000000s the error rate drops considerably. It would be interesting to calculate the actual error rate. – Moop Aug 27 '14 at 19:08

## Perl 5, 938988877563 44

$/=($/<1)-$/while$_+$/-reverse$_+$/;$_=$/+0  Ungolfed: while($input + $adjustment - reverse($input + $adjustment)) {$adjustment = ($adjustment < 1) -$adjustment;
}
$input =$adjustment + 0;  ## gives 0 if $adj is undefined (when$input is a palindrome)
print $input; ## implicit  Thanks to Dennis's suggestions, got it down to 43 + -p = 44 • 1. -$a is shorter than $a*-1. 2. If you use ($a<1), there's no need for ? :$a++. 3. If you use the -p switch, $_=<> and print$_ is implicit, so you can drop the first statement and change the last to $_=$a+0. – Dennis Aug 28 '14 at 21:55 • @Dennis Nice finds. This is only my second attempt at code golf, so appreciate the advice! – user0721090601 Aug 28 '14 at 22:02 • It's customary to count the -p switch as one extra byte, but you can get it back by using ($a<1)-$a instead of -$a+($a<1). – Dennis Aug 28 '14 at 22:52 • @Dennis I though about using that method based on your answer above, but the gain gets lost because it requires a space before while – user0721090601 Aug 28 '14 at 22:56 • If you use $/ instead of $a, it will work. – Dennis Aug 28 '14 at 23:01 # 05AB1E, 15 14 bytes (-1 Thanks to Emigna) 2äнsgÈi∞ë.∞}s-  Try it online! # Method: • Take the first half of the number. • Mirror it intersected if odd, non-intersected if even. • Difference. • I think you can use 2äн instead of g;î£. – Emigna Dec 4 '17 at 14:48 # Java : 127 109 Basic iteration, checking both negative and positive before moving to the next candidate. int p(long n){int i=0;for(;!(n+i+"").equals(new StringBuilder(n+i+"").reverse()+"");i=i<1?-i+1:-i);return i;}  For input 123456789012345, it returns -1358024, to equal palindrome 123456787654321. Line breaks: int p(long n){ int i=0; for(;!(n+i+"").equals(new StringBuilder(n+i+"").reverse()+"");i=i<1?-i+1:-i); return i; }  • Does n+i+"" work and save the brackets? I think that the precedence should be correct. – Peter Taylor Aug 27 '14 at 14:45 • @PeterTaylor Yep, and got another few from toString(). Thanks :) – Geobits Aug 27 '14 at 14:53 • Can I steal that sweet i=i<1?-i+1:-i? I shall call it "indecrement". – Jacob Aug 28 '14 at 9:19 • @Jacob Go for it ;) – Geobits Aug 28 '14 at 12:32 # Clojure, 92 Takes the first from a lazy for-sequence that works from 0 out and only includes values that make palindromes: (defn p[x](first(for[i(range)j[1 -1]k[(* i j)]s[(str(+ x k))]:when(=(seq s)(reverse s))]k)))  REPL-LPER session: golf-flog> (p 3) 0 golf-flog> (p 10) 1 golf-flog> (p 234) -2 golf-flog> (p 1299931) -10 golf-flog> (p (bigint 1e15)) 1  # JavaScript, 175136 117 Straightforward. p returns true if a given number is palindrome, f searches the nearest. EDIT: I also golfed it a little bit more thanks to the sweet "indecrement" trick by Geobits in the Java answer here. p=function(n){return (s=''+n).split('').reverse().join('')==s} f=function(n){for(i=0;!p(n+i);i=i<1?-i+1:-i);return i}  Usage: f(3) f(234) f(1299931)  • 104 in ES6: p=n=>[...s=''+n].reverse().join('')==s f=n=>{r=t=0;while(!(p(n+r++)||p(n+t--)));return p(n+r-1)?r-1:t+1} :) – William Barbosa Aug 27 '14 at 19:09 • I bet it is. function and return are terribly long reserved-words... – Jacob Aug 27 '14 at 19:12 • Sorry for the 3-year delay, but golfed to 68 in ES6: s=>{for(i=0;[...s+i+""].reverse().join!=s+i;i=i<0?-i:~i);r‌​eturn i}. Stack-overflow prone 61: f=(s,i=0)=>[...s+i+""].reverse().join==s+i?i:f(s,i<0?-i:~i‌​) ;) – Shieru Asakoto Dec 7 '17 at 2:20 # J - 49 char A function mapping integers to integers. ((0{g#f)>:@]^:(+:/@g=.(-:|.)@":@+f=._1 1*])^:_&0)  Here's how you might build to this result, in three parts. This is the display of the J REPL: indented lines are user input and outdented ones are REPL output. And yes, J spells the negative sign with an underscore _.  236 (_1 1*]) 4 NB. -ve and +ve of right arg _4 4 236 (f=._1 1*]) 4 NB. name it f _4 4 236 (+f=._1 1*]) 4 NB. add left to each 232 240 236 (":@+f=._1 1*]) 4 NB. conv each to string 232 240 236 ((-:|.)@":@+f=._1 1*]) 4 NB. palindrome? on each 1 0 236 (g=.(-:|.)@":@+f=._1 1*]) 4 NB. name it g 1 0 236 (+:/@g=.(-:|.)@":@+f=._1 1*]) 4 NB. logical NOR (result 1 if both=0) 0 palin =: (+:/@g=.(-:|.)@":@+f=._1 1*]) 236 (>:@]) 0 NB. increment right 1 236 (>:@]^:2) 0 NB. functional power 2 236 (>:@]^:(236 palin 3)) 3 NB. power 1 if no palindromes 4 236 (>:@]^:(236 palin 4)) 4 NB. power 0 if has palindrome 4 236 (>:@]^:palin) 4 NB. syntactic sugar 4 236 (>:@]^:palin^:_) 0 NB. increment until palindrome, start with 0 4 (>:@]^:(+:/@g=.(-:|.)@":@+f=._1 1*])^:_&0) 236 NB. bind 0 4 delta =: >:@]^:(+:/@g=.(-:|.)@":@+f=._1 1*])^:_&0 ((f) delta) 236 NB. f=: -ve and +ve _4 4 ((g) delta) 236 NB. g=: which are palindromes 1 0 ((g#f) delta) 236 NB. select the palindromes _4 ((g#f) delta) 126 NB. what if both are equal? _5 5 ((0{g#f) delta) 126 NB. take the first element _5 ((0{g#f)>:@]^:(+:/@g=.(-:|.)@":@+f=._1 1*])^:_&0) 236 NB. it works! _4  Examples:  pal =: ((0{g#f)>:@]^:(+:/@g=.(-:|.)@":@+f=._1 1*])^:_&0) pal 3 0 pal every 234 1299931 126 _2 _10 _5 pal 2424 18 2424 + pal 2424 2442  You can also make the golf prefer the positive solution over the negative when they're equal, by changing _1 1 to 1 _1. # Javascript 86 n=>{s=(n+'').split('');for(i=0,j=s.length-1;i<j;i++,j--)s[j]=s[i];return s.join('')-n}  This is my first codegolf challenge. Hope this solution is acceptable. ungolfed:  n => { s = (n + '').split(''); for (i = 0, j = s.length - 1; i < j; i++,j--) s[j] = s[i]; return s.join('') - n }  Explanation: Convert input n to String and split. Iterate over both sides of the resulting array and copy digit on s[i] to s[j] until i < j. This will result in our desired palindrome. Join array back together and subtract n to get x • Welcome to PPCG! This answer has the right structure (function submissions normally work best in JavaScript), and seems to give the right answers too. Your post might be improved via an explanation of why this algorithm works (it's not obvious to me why it does), but it's fine at the moment. – user62131 Feb 23 '17 at 12:45 • Thanks, ive added a small explanation and an ungolfed version – Beldraith Feb 23 '17 at 13:19 • you can change s=(n+'').split('') to s=[...(n+'')]. to shave off 5 bytes – Brian H. Nov 21 '17 at 12:06 • I was thinking the same way, but 19 seems to be the first counterexample: f(19)=3 because 22 is closest palindromic, but the function returns -8 for converting 19 into 11. btw [...n+''] will also work for an extra -2 bytes – Shieru Asakoto Dec 7 '17 at 1:42 # JavaScript (ES6), 84 bytes n=>[...(''+n)].reduce((p,c,i,s,m=s.length-1)=>i<m/2?p+(c-s[m-i])*Math.pow(10,i):p,0)  My first golf challenge! I know the shorter and more elegant solution has already been posted by @Brian H., but this is another approach. ### Test Code const t = n=>[...(''+n)].reduce((p,c,i,s,m=s.length-1)=>i<m/2?p+(c-s[m-i])*Math.pow(10,i):p,0) ; console.log('t(3) =', t(3)); // expected: 0 console.log('t(234) =', t(234)); // expected: -2 console.log('t(1299931) =', t(1299931)); // expected: -10 console.log('t(126) =', t(126)); // expected: -5 • Welcome to PPCG! – Steadybox Nov 23 '17 at 21:51 # Brachylog, 8 bytes ;.≜+A↔A∧  Try it online! The label predicate ≜ is vital here, because by using it on the output before anything else happens (although it's really being invoked on the list containing the input and the output), its absolute value is minimized, because instead of doing anything smarter based on the constraints the program guesses every integer starting from 0 until it can find one that works. If ≜ is omitted, it dawns on the program that 0 is a very nice palindrome, and it will always output the negative of the input.  The input ; + plus . the output ≜ which is instantiated immediately A is A ↔ which reversed A is still A ∧ but isn't necessarily the output.  ## Groovy - 131111 107 chars Golfed: n=args[0] as long;a=n;b=n;f={if("$it"=="$it".reverse()){println it-n;System.exit 0}};while(1){f a++;f b--}  sample runs: bash-2.02$ groovy P.groovy  0
0
bash-2.02$groovy P.groovy 234 -2 bash-2.02$ groovy P.groovy  1299931
-10
bash-2.02$groovy P.groovy 123456789012345 -1358024  Ungolfed: n=args[0] as long a=n b=n f={ if("$it"=="$it".reverse()) { println it-n System.exit 0 } } while(1) { f a++ f b-- }  # Python 2 - 76 i=input() print sorted([r-i for r in range(2*i)ifr==r[::-1]],key=abs)[0]  Gets the input number and generates a list of the differences between the input and every number between 0 and 2*i only if the number is palindromic. It then sorts the list by absolute value and prints the first element. • I don't think range(2*i) will work for large inputs. – Moop Aug 27 '14 at 20:13 • You can use min with a keyword argument rather than sorting. – xnor Aug 27 '14 at 21:00 • To use ranges that long, you need to switch to xrange, which is a generator, and min, which short-circuits, to avoid overrunning your memory. – isaacg Aug 28 '14 at 1:56 ## C++ 289 Function P checks for palindromes using <algorithm> method. Ungolfed: bool P(int32_t i) { string a,b; stringstream ss; ss<<i; ss>>a; b=a; reverse_copy(b.begin(),b.end(),b.begin()); int k=a.compare(b); return (k==0); } int main() { int32_t n; cin>>n; int32_t x=0,y=n,z=n,ans=x; while(1) { if(P(y)){ans=x; break;} if(P(z)){ans=-1*x; break;} x++; y+=x; z-=x; } cout<<ans<<endl; return 0; }  • It will be shorter to put everything on one line. – cat Jun 24 '16 at 13:01 ## Mathematica 75 Probably can be golfed more.. p = (j=0; b=#; While[a=IntegerDigits[b]; b += ++j(-1)^j; a!=Reverse[a]]; #-b+(-1)^j) &  Spaces not counted and not needed. # CoffeeScript: 73 (x)->(x+="")[0...(y=x.length/2)]+x[0...-y].split("").reverse().join("")-x  Explanation: This takes advantage of the fact that if we have a number of odd length (say 1234567), x.slice(0, y) won't include the middle digit but x.slice(0, -y) will. JavaScript's slice probably shouldn't work this way, but it does. I was expecting CoffeeScript/JavaScript to have a better way to reverse a string, but the split/reverse/join method seems to be all there is. # PHP, 56 bytes for(;strrev($i+$n=$argv[1])-$n-$i;$i=($i<1)-$i);echo+$i;


takes input from command line argument; run with -nr.

# javascript 68 bytes

(n,s=[...(''+n)],j=s.length)=>s.map((v,i,)=>i>--j?s[j]:v).join('')-n


HUGE props to @Beldraith for the algorithm, i'm posting this as an answer though, because it took me quite the time to get it to work in a single statement.

Any tips are welcome ;)

### ungolfed

(
n, // input
s=[...(''+n)], // input split to array of chars
j=s.length, // highest available index in s
)=>
s.map( // this will return a new array, without modifying s
(
v, // value of current iteration
i, // index of current iteration
)=> i > --j ? s[j] : v
).join('') - n

• @Beldraith hope you dont mind me porting your answer to a single statement function, i had a blast doing so :D – Brian H. Nov 21 '17 at 13:21
• Golfable to 63: (n,s=[...n+''],j=s.length)=>s.map((v,i)=>i>--j?s[j]:v).join-n, but also a non-obvious counterexample (19) exists ;) – Shieru Asakoto Dec 8 '17 at 3:03
• ouch, it's not just 19, it's any number that ends with a 9 and should get a positive result – Brian H. Dec 11 '17 at 10:02

Python, 109

def q(x,z):
r=lambda s:int(str(s)[::-1])
if x+z==r(x+z):return z
if x-z==r(x-z):return -z
return q(x,z+1)

• this throws an error when running (maximum recursion depth exceeded) – Moop Aug 27 '14 at 17:47
• That's not an error in my code. It will exceed maximum recursion depth on a massive number, but it works on decently sized numbers. As there was no maximum test case in the specs, this should still be considered a valid solution. – RageCage Aug 27 '14 at 18:10
• The number 123456789 causes it to fail, well below the 10^15 limit posted in the question. – Moop Aug 27 '14 at 18:13
• You could easily turn the recursion into a loop and avoid this issue altogether – Moop Aug 27 '14 at 18:15
• Running this in the Stackless Python implementation should avoid the recursion depth issue. – xnor Aug 27 '14 at 19:26

## QBIC, 38 bytes, nc

:{[-1,1,2|A=!a+b*c$~A=_fA||_xb*c]c=c+1  Explanation: The code reads an input, and then applies a modifier. It then tests to see if the number + modifier is a palindrome. Then, it flips the sigh on the modifier, re-applies that and tests again. :{ Read the input value, start a DO-loop [-1,1,2| FOR (b = -1; b <= 1; b+=2 ) A=!a+b*c$ Get a string from the input number,
plus modifier c (which is 0 at the start of QBIC)
times -1 or 1, depending on b's iteration.
~A=_fA|   if that string is equal to it's own reversed version
|_xb*c]   then Quit, printing the modifier * sign
c=c+1     Increment the modifoer and DO-LOOP again.
The DO-loop is implicitly closed by QBIC at EOF


# Bash, 73 bytes

i=$1;x=$i;while((x-10#$(rev<<<$x)));do ((r=(1>r)-r,x=r+i));done;echo \$x


Input goes to the 1st command line argument:

foo.sh 123456789


# Axiom, 720594 412 bytes

R(x)==>return x;p(r,a)==(n:=#(a::String);if r<0 then(a=0=>R a;n=1 or a=10^(n-1)=>R(a-1);a=10^(n-1)+1=>R(a-2));if r>0 then(n=1 and a<9=>R(a+1);a=10^n-1=>R(a+2));r=0 and n=1=>1;v:=a quo 10^(n quo 2);repeat(c:=v;w:=(n rem 2>0=>v quo 10;v);repeat(c:=10*c+w rem 10;w:=w quo 10;w=0=>break);r<0=>(c<a=>R c;v:=v-1);r>0=>(c>a=>R c;v:=v+1);R(c=a=>1;0));c)
D(a:NNI):INT==(p(0,a)=1=>0;w:=p(-1,a);s:=p(1,a);a-w<s-a=>w-a;s-a)


The byte count it is again this, but the algo it would be O(log(n)) because it would dipend only from the digit lenght of its input (and log10(n) would be near the lenght of the decimal digits of n). ungolfed and results

-- Ritorna il precedente numero palidrome rispetto ad 'a' NNI, se r<0
--                               ha la particolarita' palpn(-1,0) = 0
-- Ritorna il successivo numero palidrome rispetto ad 'a' NNI, se r>0
-- Se r=0 ritorna 1 se 'a' e' palindrome, 0 se 'a' non e' palindrome
R(x)==>return x
palpn(r,a)==
n:=#(a::String) -- n la lunghezza in cifre di base 10 di a
if r<0 then(a=0        =>R a;n=1 or a=10^(n-1)=>R(a-1);a=10^(n-1)+1=>R(a-2))
if r>0 then(n=1 and a<9=>R(a+1);    a=10^n-1  =>R(a+2))
r=0  and n=1=>1
v:=a quo 10^(n quo 2)
repeat -- because here not there is a goto instruction i have to use repeat
c:=v;w:=(n rem 2>0=>v quo 10;v)
repeat
c:=10*c+w rem 10
w:=w quo 10
w=0=>break
r<0=>(c<a=>R c;v:=v-1)
r>0=>(c>a=>R c;v:=v+1)
R(c=a=>1;0) -- for r==0
c

-- Ritorna la distanza minima tra l'input 'a' e una palindrome:
--        0 se 'a' e' una palindrome
--        r numero con segno negativo se tale palindrome precede 'a'
--        r numero con segno positivo se tale palindrome e' successiva ad 'a'
palDistance(a:NNI):INT==
palpn(0,a)=1=>0
p:=palpn(-1,a);s:=palpn(1,a)
a-p<s-a=>p-a
s-a

--------------------------------------

(3) -> [[i,D(i)] for i in [3,10,234,1299931,126]]
(3)  [[3,0],[10,1],[234,- 2],[1299931,- 10],[126,5]]
Type: List List Integer
(4) -> D 7978986575546463645758676970789089064235234524548028408198401348930489104890184018410
(4)  - 199223418598327604580355025458434427119613
Type: Integer
(5) ->  p(0,7978986575546463645758676970789089064235234524548028408198401348930489104890184018410+%)
(5)  1
Type: PositiveInteger
(6) -> 7978986575546463645758676970789089064235234524548028408198401348930489104890184018410+%%(-2)
(6)
7978986575546463645758676970789089064235234325324609809870796768575463646455756898797
Type: PositiveInteger

• The ones had spoken again (or for the complete elimination) the use of goto for computer languages, for my humble hobby programmer prospective: Are incompetent in informatics !!!! – RosLuP Nov 21 '17 at 9:21

# Husk, 16 12 9 bytes

ḟoS=↔+⁰İZ


Thanks @H.PWiz for -4 bytes!

Try it online!

### Explanation

ḟ(S=↔+⁰)İZ  -- input ⁰ a number, for example: 126
İZ  -- built-in integers: [0,1,-1,2,-2...]
ḟ(     )    -- first element that satisfies the following (eg. 5):
+⁰     --   add element to input: 131
S=        --   is it equal to itself..
↔       --   ..reversed: 131 == 131


# APL NARS 47 chars

r←s a;b
r←0
A:b←⍕a+r⋄→0×⍳b≡⌽b⋄r←-r⋄→A×⍳r<0⋄r+←1⋄→A


this above search but algo can not be fast and right as the g below...

This

A:b←⍕a+r⋄→0×⍳b≡⌽b⋄r←-r⋄→A×⍳r<0⋄r+←1⋄→A


is a simple loop exit only when it find b≡⌽b so b is a string palindrome

  s¨3,10,234,1299931,126
0 1 ¯2 ¯10 5

∇r←g w;n;a;y;t;o;h;v
r←0J1
→0×⍳0≠⍴⍴w⋄→0×⍳''≡0↑w ⍝ if arg is not scalar int>=0→0J1
→0×⍳(w<0)∨w≠⌊w
h←{z←⍕⍺⋄q←⍕⍵⋄⍎(z,⌽q)}⍝ h return as digit ⍺⌽⍵
n←⍴⍕w⋄r← 0
→0×⍳n≤1              ⍝ arg one digit return r←0
a←10*⌊n÷2
B: v←a⋄→C×⍳∼2∣n⋄v←a×10
C: t←⌊w÷v ⋄y←⌊w÷a
o←y h t⋄r←(y+1)h t+1
→D×⍳∼(∣r-w)<∣o-w⋄r←r-w⋄→0
D: r←o-w
∇

g¨3,10,234,1299931,126
0 1 ¯2 ¯10 ¯5


# Python 2, 55 54 bytes

l=lambda n,d=0:n+d!=n+d[::-1]and l(n,~d+(d<0))or d


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# Japt, 8 bytes

nÈ¥sw}cU


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nÈ¥sw}cU     :Implicit input of integer U
cU     :Get the first number in the sequence [U,U-1,U+1,U-2,U+2,...,U-n,U+n]
È           :That returns true when passed the the following function
¥          :  Test for equality with
s         :  Convert to string
w        :  Reverse
}       :End function
n            :Subtract U from the result