Minimum multiple of m where digital sum equals m

Minimum multiple of m where digital sum equals m is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

Generate the sequence a(n) when each element is the minimum integer multiple m such that the digit sum of n times m is equal to n.

Task

• Find the first 40 elements of the sequence.

Stretch

• Find the next 30 elements of the sequence.

See also

• OEIS:A131382 - Minimal number m such that Sum_digits(n*m)=n

ALGOL 68

<lang algol68>BEGIN # find the smallest m where mn = digit sum of n, n in 1 .. 70 #

   # returns the digit sum of n, n must be >= 0 #
   OP   DIGITSUM = ( INT n )INT:
        IF  n < 10 THEN n
        ELSE
           INT result := n MOD  10;
           INT v      := n OVER 10;
           WHILE v > 0 DO
               result +:= v MOD  10;
               v       := v OVER 10
           OD;
           result
        FI # DIGITSUM # ;
   # show the minimum multiples of n where the digit sum of the multiple is n #
   FOR n TO 70 DO
       BOOL found multiple := FALSE;
       FOR m WHILE NOT found multiple DO
           IF DIGITSUM ( m * n ) = n THEN
               found multiple := TRUE;
               print( ( " ", whole( m, -8 ) ) );
               IF n MOD 10 = 0 THEN print( ( newline ) ) FI
           FI
       OD
   OD

END</lang>

Output:

        1        1        1        1        1        1        1        1        1       19
       19        4       19       19       13       28       28       11       46      199
       19      109       73       37      199       73       37      271      172     1333
      289      559     1303      847     1657      833     1027     1576     1282    17497
     4339     2119     2323    10909    11111    12826    14617    14581    16102   199999
    17449    38269    56413    37037  1108909   142498   103507   154981   150661  1333333
   163918   322579   315873   937342  1076923  1030303   880597  1469116  1157971 12842857

Phix

Translation of: XPL0

with javascript_semantics
integer c = 0, n = 1
while c<70 do
    integer m = 1
    while true do
        integer nm = n*m, t = 0
        while nm do
            t += remainder(nm,10)
            nm = floor(nm/10)
        end while
        if t=n then exit end if
        m += 1
    end while
    c += 1
    printf(1,"%-8d%s",{m,iff(remainder(c,10)=0?"\n":"")})
    n += 1
end while

Output:

1       1       1       1       1       1       1       1       1       19
19      4       19      19      13      28      28      11      46      199
19      109     73      37      199     73      37      271     172     1333
289     559     1303    847     1657    833     1027    1576    1282    17497
4339    2119    2323    10909   11111   12826   14617   14581   16102   199999
17449   38269   56413   37037   1108909 142498  103507  154981  150661  1333333
163918  322579  315873  937342  1076923 1030303 880597  1469116 1157971 12842857

Raku

<lang perl6>sub min-mult-dsum ($n) { (1..∞).first: (* × $n).comb.sum == $n }

say .fmt("%2d: ") ~ .&min-mult-dsum for flat 1..40, 41..70;</lang>

Output:

 1: 1
 2: 1
 3: 1
 4: 1
 5: 1
 6: 1
 7: 1
 8: 1
 9: 1
10: 19
11: 19
12: 4
13: 19
14: 19
15: 13
16: 28
17: 28
18: 11
19: 46
20: 199
21: 19
22: 109
23: 73
24: 37
25: 199
26: 73
27: 37
28: 271
29: 172
30: 1333
31: 289
32: 559
33: 1303
34: 847
35: 1657
36: 833
37: 1027
38: 1576
39: 1282
40: 17497
41: 4339
42: 2119
43: 2323
44: 10909
45: 11111
46: 12826
47: 14617
48: 14581
49: 16102
50: 199999
51: 17449
52: 38269
53: 56413
54: 37037
55: 1108909
56: 142498
57: 103507
58: 154981
59: 150661
60: 1333333
61: 163918
62: 322579
63: 315873
64: 937342
65: 1076923
66: 1030303
67: 880597
68: 1469116
69: 1157971
70: 12842857

Wren

Library: Wren-math

Library: Wren-seq

Library: Wren-fmt

<lang ecmascript>import "./math" for Int import "./seq" for Lst import "./fmt" for Fmt

var res = [] for (n in 1..70) {

   var m = 1
   while (Int.digitSum(m * n) != n) m = m + 1
   res.add(m)

} for (chunk in Lst.chunks(res, 10)) Fmt.print("$,10d", chunk)</lang>

Output:

         1          1          1          1          1          1          1          1          1         19
        19          4         19         19         13         28         28         11         46        199
        19        109         73         37        199         73         37        271        172      1,333
       289        559      1,303        847      1,657        833      1,027      1,576      1,282     17,497
     4,339      2,119      2,323     10,909     11,111     12,826     14,617     14,581     16,102    199,999
    17,449     38,269     56,413     37,037  1,108,909    142,498    103,507    154,981    150,661  1,333,333
   163,918    322,579    315,873    937,342  1,076,923  1,030,303    880,597  1,469,116  1,157,971 12,842,857

XPL0

<lang XPL0>func SumDigits(N); \Return sum of digits in N int N, S; [S:= 0; while N do

   [N:= N/10;
   S:= S + rem(0);
   ];

return S; ];

int C, N, M; [C:= 0; N:= 1; repeat M:= 1;

       while SumDigits(N*M) # N do M:= M+1;
       IntOut(0, M);
       C:= C+1;
       if rem (C/10) then ChOut(0, 9\tab\) else CrLf(0);
       N:= N+1;

until C >= 40+30; ]</lang>

Output:

1       1       1       1       1       1       1       1       1       19
19      4       19      19      13      28      28      11      46      199
19      109     73      37      199     73      37      271     172     1333
289     559     1303    847     1657    833     1027    1576    1282    17497
4339    2119    2323    10909   11111   12826   14617   14581   16102   199999
17449   38269   56413   37037   1108909 142498  103507  154981  150661  1333333
163918  322579  315873  937342  1076923 1030303 880597  1469116 1157971 12842857