# It's all in the title...

Take as input a positive integer n>=12 and... do what the title says.

Yes, this is on OEIS A187924.

Some test cases

12 -> 912
13 -> 11713
14 -> 6314
15 -> 915
16 -> 3616
17 -> 15317
18 -> 918
19 -> 17119
20 -> 9920
40 -> 1999840
100-> 99999999999100


This is . Shortest code in bytes wins!

• Comments are not for extended discussion; this conversation has been moved to chat. – Martin Ender Dec 9 '17 at 14:12
• To close up a part of what was moved to chat: my edit to the OEIS proving that 11 is the only number without a solution was just approved. – Ørjan Johansen Jan 21 '18 at 4:55

# Befunge, 81 bytes

&>00p0v<!%g0<
v%"d":_>1+:0^
>00g->#^_:0v
0g10g-#^_.@1>
>0p:55+/\:v>
^1+g01%+55_$^  Try it online! Can handle up to n = 70 at least, after which some values will start overflowing the stack cell size on most implementations, and on those that don't, it'll take so long that it's not worth waiting to find out. Given those constraints, we don't even bother trying to handle values of n greater than 99, which means we can more easily test if the value ends in n with by simply comparing the value modulo 100 with n. Below is more detailed breakdown of the code.  Read n from stdin and save in memory. Initialize the test value v to 0 and start the main loop, incrementing v up front. Test if v%n == 0, and if not return to the start of the main loop. Test if v%100 == n, and if not return to the start of the main loop. Sum the digits in v by repeatedly adding v modulo 10 and dividing v by 10. Test if the sum is equal to n, and if not return to the start of the main loop. Otherwise output v and exit. ## JavaScript (ES6), 55 54 bytes f=(s,p=0,a=p+s)=>a%s|eval([...a].join+)-s?f(s,p+1):a <input type=number min=12 oninput=o.textContent=f(this.value)><pre id=o> Takes input as a string. Needs a browser with tail recursion support for the larger results. Edit: Saved 1 byte thanks to @Arnauld. • eval([s,...a].join-)? would also work, though it's not any shorter... – ETHproductions Nov 27 '17 at 14:57 • @Arnauld No, I just forgot that I can do that with ||. – Neil Nov 27 '17 at 15:26 # 05AB1E, 14 bytes [NI«ÐIÖsSOIQ*#  Try it online! Explanation Solutions requiring large prefixes will time out on TIO [ # start a loop NI« # append input to current iteration number Ð # triplicate IÖ # is the first copy evenly divisible by input? sSOIQ # is the digit sum of the second copy equal to the input? * # multiply # # if true, break loop # output the third copy  • If feel as if 05AB1E is cheating, because it's so good. The only way to beat this by a mile would be to make a programming 'compression' language that references past language. I submit ans = dic lol – PathToLife Nov 27 '17 at 14:40 • @Pathfinder: There are a couple of languages out there that can consistently beat 05AB1E, so we can still hope to see something even shorter :) – Emigna Nov 27 '17 at 15:04 • My attempt: ∞.Δ©IÅ¿®IÖ®SOIQP – Makonede Apr 2 at 19:46 # Brachylog v2, 12 10 bytes a₁.;A×?≜ẹ+  Try it online! This is a function submission that takes input via . and produces output via ? (the opposite of the normal convention; all Brachylog functions have exactly two arguments, which can be input or output arguments, but the language doesn't enforce any particular argument usage). We don't normally consider conventions for argument usage to be relevant at PPCG. ## Explanation A previous version of this solution had a special case (Ḋ|, i.e. "return digits literally") for single digits, but the question apparently states that you don't have to check for that (thanks @DLosc for catching this), so I removed it. (The solution as written won't work on single digits as Brachylog won't consider 1 as a possibility for an unknown in a multiplication, to prevent infinite loops; its multiplications are arbitrary-arity.) So this answer now goes for a pretty much direct translation of the specification. Starting with ? (the output / number we're trying to find; a Brachylog predicate always implicitly starts with ?) we use a₁. to assert that it has . (the input) as a suffix. Then ;A×? means that we can multiply (×) the result by something (;A) to produce ? (the output). Finally, ẹ+ sums (+) the digits (ẹ) of ?, and there's by default an implicit assertion at the end of every Brachylog program that the final result produces .. So in other words, this program is ". is a suffix of ?, . multiplied by something is ?, . is the digit sum of ?", which is very close to a literal translation of the original program. The ≜ is necessary for the digit sum requirement to be enforced. I assume something about ẹ doesn't like unknowns, so the ≜ tells Brachylog to use a brute-force approach for that part of the program rather than algebra. # Haskell, 72 bytes f n=[x|x<-[n,n+lcm n(10^length(show n))..],sum[read[j]|j<-show x]==n]!!0  Try it online! Note that the found number minus n must be a multiple of both n and 10^length(n). Inspired by Laikoni and totallyhuman • Welcome to the site! – DJMcMayhem Nov 27 '17 at 17:03 • Change lcm n(10^length(show n)) to lcm(10^length(show n))n for 1 byte – H.PWiz Nov 27 '17 at 19:52 ## Alice, 35 bytes /o \i@/!w?+.?~\ & /-$K..?\ L z $/K  Try it online! ### Explanation This program has a really nice mix and interaction between Cardinal (integer-processing) and Ordinal (string-processing) mode. The usual framework for challenges with decimal I/O which operate largely in Cardinal mode: /o \i@/...  And the actual program: ! Store the input N on the tape. We'll use an implicit zero on top of the stack as our iterator variable X, which searches for the first valid result. w Store the current IP position on the return address stack. This marks the beginning of the main search loop. We can avoid the divisibility test by going up in increments of N. To check the other two conditions, we'll use individual conditional loop ends that skip to the next iteration. Only if both checks pass and all loop ends are skipped will the search terminate. ?+ Increment the iterator X by N. . Duplicate X. ?~ Put a copy of N underneath. \ Switch to Ordinal mode. & Implicitly convert X to a string, then fold the next command over its characters, i.e. its digits. Here, "fold" means that each character is pushed to the stack in turn, followed by one execution of that next command. / Switch back to Cardinal mode (this is not a command). - Fold subtraction over the digits. This implicitly converts each digit back to its numerical value and subtracts it from N. If the digit sum of X is equal to N, this will result in 0.$K    Jump back to the w if the digit sum of X isn't N.
..    Duplicate X twice.
?     Get a copy of N.
\     Switch to Ordinal mode.
L     Shortest common superstring. Implicitly converts X and N to strings
and gives the shortest string that starts with X and ends with N.
This will be equal to X iff X already ends with N. Call this Y.
z     Drop. If X contains Y, this deletes everything up to and including
Y from X. This can only happen if they are equal, i.e. if X ended
with N. Otherwise X remains unchanged.
$Skip the next command if the string is empty, i.e. if X ended with N. / Switch back to Cardinal mode. K Jump back to w if X didn't end with N.  # Java (OpenJDK 8), 136110103 92 bytes -26 thanks to JollyJoker -7 again thanks to JollyJoker -11 thanks to Oliver Grégoire a->{for(int i=a;!(""+a).endsWith(""+i)|i!=(""+a).chars().map(x->x-48).sum();a+=i);return a;}  Try it online! Gotta love Java! It could well be that I am using an inefficient approach, but not having a built in checksum function and the double conversion to String to check for the end of the number costs bytes... Ungolfed:  a->{ //input n (as integer) for (int i = a; //initiate loop !("" + a).endsWith("" + i) //check if the calculated number ends with the input | i != ("" + a).chars().map(x -> x - 48).sum(); //check if the checksum is equal to the input a += i) //for every iteration, increase i by the input to save checking for divisibility ; //empty loop body, as everything is calculated in the header return a; //return number }  • (""+i).endsWith(""+a) should work. – JollyJoker Nov 28 '17 at 8:28 • @JollyJoker brilliant, thanks for making me feel stupid :P – Luca H Nov 28 '17 at 8:38 • Heh. n/=10 instead of n=n/10 too. Also, i+=a in the for loop so you can skip the divisibility check. – JollyJoker Nov 28 '17 at 8:50 • @JollyJoker wow, I did it for the sum but not for the division... Thank you, I'll add it shortly – Luca H Nov 28 '17 at 8:54 • 92 bytes, using the API, shorter than calculating yourself. Also, the semicolon is not part of the bytecount because a valid lambda can be given as method argument, for instance and then you don't need that semicolon. – Olivier Grégoire Nov 28 '17 at 11:06 # Mathematica, 72 bytes (t=#;While[Mod[t,10^IntegerLength@#]!=#||Tr@IntegerDigits@t!=#,t+=#];t)&  -18 bytes from @MartinEnder Try it online! Here is another version from Martin Ender This approach can go up to n=40 (41 exceeds the default iteration limit) # Mathematica, 65 bytes #//.t_/;Mod[t,10^IntegerLength@#]!=#||Tr@IntegerDigits@t!=#:>t+#&  Try it online! # Husk, 20 19 17 bytes ḟȯ=⁰Σdfȯ€d⁰ṫdm*⁰N  Thanks @Zgarb for -2 bytes! Try it online! • 17 bytes by splitting the condition into two. – Zgarb Nov 27 '17 at 17:53 # Python 2, 74 bytes This solution assumes that n <= sys.maxint. n=x=input() while sum(map(int,str(x)))-n*str(x).endswith(n):x+=n print x  Try it online! • Replace str(x) with x in back-ticks two times to save 6 bytes (how do you escape back-ticks inside back-ticks?). – Chas Brown Nov 28 '17 at 9:44 • @ChasBrown  backslash tick inside backticks. – wvxvw Nov 28 '17 at 12:34 • @ChasBrown no, as for long integers that would add an L which could mess up the algorithm. – FlipTack Nov 28 '17 at 18:37 # C (gcc) 71 69 bytes , fails on 100 I tried with long and %1000 but times out -2 bytes thanks to steadybox s,i,j;f(n){for(j=0;s^n|j%100!=n;)for(s=0,i=j+=n;i;i/=10)s+=i%10;j=j;}  Try it online # C# (.NET Core), 90 84 83 + 18 = 101 bytes using System.Linq; n=>{for(int i=n;!(""+n).EndsWith(""+i)|n%i>0|(""+n).Sum(c=>c-48)!=i;n++);return n;}  Try it online! • 6 bytes saved thanks to Emigna and my uncanny ability to write (""+n) in some places and n.ToString() in others. • n=>{for(int i=n;n%100!=i|n%i>0|(""+n).Sum(c=>c-'0')!=i;n++);return n;} saves 20 bytes. – Emigna Nov 27 '17 at 11:28 • @Emigna why n%100? What if n>100? – Charlie Nov 27 '17 at 11:37 • Oh yeah, ignore that part. That was from testing with 2-digit input. The mod would have to be 10^len(input). Probably not worth it then. – Emigna Nov 27 '17 at 12:31 # Ohm v2, 16 bytes £^›u³↔ξ³¥s}Σ³E*‽  Try it online! # JavaScript REPL (ES5), 60 59 bytes for(n=prompt(i=0);eval([].join.call(t=++i+n,'+'))-n|t%n;);t  • @totallyhuman Fixed – l4m2 Nov 28 '17 at 23:51 • In console it outputs without alert() so I guess – l4m2 Nov 28 '17 at 23:52 # Julia, 70 bytes f(x)=(n=x;while(sum(digits(n))!=x||x!=n%(10^length("$x")));n+=x;end;n)

• ¬x=(n=x;while sum(digits(n))!=x||!endswith("$n","$x");n+=x;end;n) You can save 5 bytes with this. Try it online! – LukeS Dec 22 '17 at 13:08

# Pip, 18 bytes

T!y%a&$+y=aY++i.ay  Algorithm inspired by Emigna's answer. Try it online! ### How it works  a is 1st cmdline arg, i is 0, y is "" (implicit) T Loop until !y%a& y%a is 0 and$+y=a         sum of y is a:
++i      Increment i
Y   .a    and yank (i concat a) into y
y  After the loop exits, autoprint y


## Scala, 120 bytes

def a(n:Int)={val b=math.pow(10,math.ceil(math.log10(n))).##;var c=b+n;while(c%n!=0||(0/:c.toString)(_+_-'0')!=n)c+=b;c}


This works until n = 70, after which integers overflow. For one extra character, the Int can change to a Long and allow values for n > 100 to be computed.

Here is the slightly longer ungolfed version:

def golfSourceLong(n: Long): Long = {
val delta = math.pow(10, math.ceil(math.log10(n))).toInt
var current = delta + n
while (current % n != 0 || current.toString.foldLeft(0)(_ + _ - '0') != n) {
current += delta
}
current
}


# Python 2, 70 bytes

f=lambda n,x=0:x*(x%n<sum(map(int,x))==n==x%10**len(n))or f(n,x+n)


Try it online!

# Stax, 16 bytes

è}╘⌐ƒw┴L≤⌂IÑ═eαü


Run and debug it

f n=[x|x<-[0,n..],sum[read[d]|d<-show x]==n,mod x(10^length(show n))==n]!!0


Try it online!

Explanation:

f n=[x|                                      ]!!0 -- Given input n, take the first x
x<-[0,n..],                                -- which is a multiple of n,
sum[read[d]|d<-show x]==n,      -- has a digital sum of n
mod x(10^length(show n))==n     -- and ends in n.


I wonder whether the "ends in n" part can be shortened. I also tried show nelemscanr(:)""(show x), but it's longer.

->n{a=n;a+=n until/#{n}$/=~a.to_s&&a.digits.sum==n;a}  Try it online! # Pyth, 22 21 bytes fq2-/,%T^;lQsjT;Q%TQ  Try it here! # Haskell, 75 bytes f n=[i|i<-[n,n+10^length(show$n)..],imodn<1,sum[read[j]|j<-show$i]==n]!!0  Try it online! # PowerShell, 84 bytes for($n=$i=$args;$i%$n-or$i-notmatch"$n$"-or([char[]]"$i"-join'+'|iex)-$n){$i++}$i  Try it online! Simple construction but lengthy commands. Times out on TIO for n=100, but if we explicitly set i to be close, it outputs correctly. This is just a simple for loop that keeps going so long as any one of the conditions is true. The three conditions are 1) $i%$n, i.e., we have a remainder; 2) $i-notmatch"$n$", i.e., it doesn't regex match the last couple of digits; and 3) ([char[]]"$i"-join'+'|iex)-$n, i.e., the digits summed together is not equal to $n (here checked by simple subtraction, since nonzero values are truthy). Inside the loop we're simply incrementing $i.

Thus, if we don't have a remainder, the regex matches, and the numbers are equal, all three conditions are $false and we exit the loop. As a result, we just can leave $i on the pipeline, and output is implicit.

# PHP, 73+1 bytes

while(array_sum(str_split($i+=$n=$argn))-$n|$i%10**strlen($n)-$n);echo$i;


Run as pipe with -R.

loops $i through multiples of <input> until sum_of_digits-<input> and tail_of_i-$n are falsy; then prints i.

# m4, 210 bytes

define(d,define)d(i,ifelse)d(s,i($1,,0,eval(substr($1,0,1)+s(substr($1,1)))')')d(k,r($1,eval($2+1))')d(r,i(s($2),$1,i(regexp($2,$1$),-1,k($1,$2)',i(eval($2%$1),0,$2,k($1,$2)')),k($1,$2)')')d(f,r($1,1)')


Defines a macro f which computes the answer. It's a bit slow—unusably so—but I promise it works.

I thought m4 would be nice because it treats integers as strings by default, but this is pretty bad.

# R, 115 bytes

function(n,d=nchar(n):1){while(sum(D<-F%/%10^((k=nchar(F)):1-1)%%10)-n|any(D[k-d+1]-n%/%10^(d-1)%%10)|F%%n)F=F+n
F}


Try it online!

Terrible R function. Increments F (starts at 0) by n until a value is found that satisfies the required properties, which it then returns. The use of any on a double expression sends out a warning for each iteration of the loop, but does not affect the correctness.

Times out on TIO for large enough inputs (n=55 or higher) but should correctly compute the solution given enough time/space.

# Perl 5, 46 44 + 1 ( -p ) = 45 bytes

2 bytes saved thanks to Xcali, couldn't find better

($\=++$t.$_)%$_|$_-eval$\=~s//+/gr.0&&redo}{


$\=++$x.$_;eval$\=~s//+/gr."-$_"|$\%\$_&&redo}{


Try it online

• Managed to save a couple bytes: Try it online! – Xcali Nov 27 '17 at 20:11

# Jelly, 22 21 bytes

DS=³a³ḍaDṫ³DLC¤Ḍ=³ø1#


Try it online!

Edit: compressed to a single line

Explanation

DS=³a³ḍaDṫ³DLC¤Ḍ=³ø1#
ø1#  Evaluate the condition before this and increment a counter until it is met then output the counter
D                      Digits of incremented variable as a list
S                     Sum
=³                   Equals argument of program?
a                  Logical and
³ḍ                Does arg divide incremented variable?
a               Logical and
Dṫ     Ḍ       Last n digits of inc. var. where n is number of digits in program input
³DLC         1 - (number of digits of program input)
=³     Equals program input?


This took me many hours to write because I'm learning Jelly but now that I'm done I'm so satisfied. For a long time I didn't realize I needed the ¤ and I just couldn't get it to work. Looking at [this] well explained code helped me seal the deal. Lots of other Jelly answers in PPCG guided me too.

• I'm afraid the [this] link is broken. – user Apr 2 at 13:51

Javascript, 224 bytes  function getNumber(x){if(x<12){return!1};const sumDigits=(x)=>x.toString().split('').map(Number).reduce((a,b)=>a+b,0);for(let i=2;i<9999;i++){if((x*i-x)%(Math.pow(10,x.toString().length))==0&&sumDigits(x*i)==x){return x*i}}}  Un-golf:

function getNumber(x){
if (x<12) {return false};
const sumDigits = (x) => x.toString().split('').map(Number).reduce((a,b)=>a+b, 0);
for (let i=2; i<9999; i++){
if((x*i-x)%(Math.pow(10, x.toString().length))==0 && sumDigits(x*i)==x){
return x*i;
}
}
}

Usage: 1. getNumber(12) 2. getNumber(13) 3. ....

• I don't know much about Javascript golfing, but I'm pretty sure you should shorten the names getNumber or sumDigits. – Ørjan Johansen Dec 4 '17 at 9:45
• Thank you so much, I am not go to win here, just want to get into this challenge :smile: – NTCG Dec 7 '17 at 4:35