Numbers with same digit set in base 10 and base 16

From Rosetta Code
Numbers with same digit set in base 10 and base 16 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.
Task

Find decimal numbers   n   that when converted to hexadecimal produce a number that uses the same set of digits (regardless of order and ignoring duplicates) as the original number,   where   n  <  100000


Example

The decimal number   2339   is   923   when written in hexadecimal.

The set of digits used,   ignoring order and duplicates,   is   {2, 3, 9}   in both cases and hence this number satisfies the task requirements.

ALGOL W

Generates the candidate numbers (ones that only have the digits 0-9 in their hexadecimal representation) to cut down the numbers to check. <lang algolw>begin % find numbers that use the same digits in decimal and hexadecimal  % 

   integer hdCount, h20, h300, h4000, h50000;
   logical array hex, dec ( 0 :: 9 );
   integer x2, x3, x4, x5, hx2, hx3, hx4, hx5;
   hdCount := 0;
   % note 100 000 is 186A0 in hexadecimal, so we need to consider numbers    %
   % with up to 5 hexadedcimal digits                                        %
   % powers of 16 %
   x2 := 16; x3 := x2 * 16; x4 := x3 * 16; x5 := x4 * 16;
   for hPos := 0 until 9 do hex( hPos ) := false;
   % construct the numbers that have only 0-9 in their hex representations   %
   for h5 := 0 until 1 do begin
       hx5 := h5 * x5;
       for h4 := 0 until 9 do begin
           hx4 := h4 * x4;
           for h3 := 0 until 9 do begin
               hx3 := h3 * x3;
               for h2 := 0 until 9 do begin
                   hx2 := h2 * x2;
                   for h1 := 0 until 9 do begin
                       integer n, d;
                       n := d := hx5 + hx4 + hx3 + hx2 + h1;
                       if n > 100000 then goto endSearch;
                       for dPos := 0 until 9 do dec( dPos ) := false;
                       if d = 0 then dec( 0 ) := true;
                       while d > 0 do begin
                           dec( d rem 10 ) := true;
                           d := d div 10
                       end while_d_gt_0 ;
                       if h5 not = 0                then hex( h5 ) := true;
                       if h5 + h4 not = 0           then hex( h4 ) := true;
                       if h5 + h4 + h3 not = 0      then hex( h3 ) := true;
                       if h5 + h4 + h3 + h2 not = 0 then hex( h2 ) := true;
                       hex( h1 ) := true;
                       if  hex( 0 ) = dec( 0 ) and hex( 1 ) = dec( 1 )
                       and hex( 2 ) = dec( 2 ) and hex( 3 ) = dec( 3 )
                       and hex( 4 ) = dec( 4 ) and hex( 5 ) = dec( 5 )
                       and hex( 6 ) = dec( 6 ) and hex( 7 ) = dec( 7 )
                       and hex( 8 ) = dec( 8 ) and hex( 9 ) = dec( 9 )
                       then begin
                           % the decimal and hexadecimal representations     %
                           % use the same digits                             %
                           writeon( i_w := 7, s_w := 0, " ", n );
                           hdCount := hdCount + 1;
                           if hdCount rem 10 = 0 then write()
                       end if_allSame ;
                       hex( h1 ) := false;
                       hex( h2 ) := false;
                       hex( h3 ) := false;        
                       hex( h4 ) := false;
                       hex( h5 ) := false;
                   end for_h5
               end for_h4
           end for_h3
       end for_h2
   end for_h1 ;

endSearch: 

   write( i_w := 1, s_w := 0, "Found ", hdCount, " numbers up to 100000 " );
   write( "      where the decimal and hexadecimal "
        , "representations use the same digits"
        );

end.</lang>

Output:
       0       1       2       3       4       5       6       7       8       9
      53     371     913    1040    2080    2339    4100    5141    5412    5441
    6182    8200    9241   13593   13665   13969   16406   20530   26946   30979
   32803   33638   33840   33841   33842   33843   33844   33845   33846   33847
   33848   33849   34883   37943   38931   38966   38995   66310   71444   71497
   71511   75120   75121   75122   75123   75124   75125   75126   75127   75128
   75129   75621   86150   88165   91465   91769   96617   98711   99481
Found 69 numbers up to 100000
      where the decimal and hexadecimal representations use the same digits

Factor

Works with: Factor version 0.99 2021-02-05

<lang factor>USING: formatting grouping io kernel math.parser present sequences sets ;

100,000 <iota> [ dup present swap >hex set= ] filter 10 group [ [ "%5d " printf ] each nl ] each</lang>

Output:
    0     1     2     3     4     5     6     7     8     9 
   53   371   913  1040  2080  2339  4100  5141  5412  5441 
 6182  8200  9241 13593 13665 13969 16406 20530 26946 30979 
32803 33638 33840 33841 33842 33843 33844 33845 33846 33847 
33848 33849 34883 37943 38931 38966 38995 66310 71444 71497 
71511 75120 75121 75122 75123 75124 75125 75126 75127 75128 
75129 75621 86150 88165 91465 91769 96617 98711 99481

Julia

The requirements seem to depend upon interpretations of set and duplicates. Hex number is shown to demonstrate how numbers fit the revised task. The revised task may or may not disallow leading zeros for the base 16 number. <lang Julia>using Combinatorics

function dheq(N) 

   found = 0
   for i in 0:N
       d = digits(i)
       dlen = length(unique(d))
       for j in 1:length(d), c in Iterators.filter(x -> length(unique(x)) == dlen,
           Combinatorics.with_replacement_combinations(d, j)), p in permutations(c)
           if evalpoly(16, p) == i && (length(p) == 1 || p[end] != 0 || count(x -> x == 0, p) > 1)
               print(rpad(i, 5), " = 0x", rpad(evalpoly(10, p), 8), (found += 1) % 5 == 0 ? "\n" : "")
               break
           end
       end
   end

end

dheq(100000)

</lang>

Output:
0     = 0x0       1     = 0x1       2     = 0x2       3     = 0x3       4     = 0x4       
5     = 0x5       6     = 0x6       7     = 0x7       8     = 0x8       9     = 0x9       
53    = 0x35      371   = 0x173     913   = 0x391     1040  = 0x410     2080  = 0x820     
2339  = 0x923     4100  = 0x1004    5141  = 0x1415    5412  = 0x1524    5441  = 0x1541    
6182  = 0x1826    8200  = 0x2008    9241  = 0x2419    13593 = 0x3519    13665 = 0x3561    
13969 = 0x3691    16406 = 0x4016    20530 = 0x5032    26946 = 0x6942    30979 = 0x7903    
32803 = 0x8023    33638 = 0x8366    33840 = 0x8430    33841 = 0x8431    33842 = 0x8432    
33843 = 0x8433    33844 = 0x8434    33845 = 0x8435    33846 = 0x8436    33847 = 0x8437
33848 = 0x8438    33849 = 0x8439    34883 = 0x8843    37943 = 0x9437    38931 = 0x9813    
38966 = 0x9836    38995 = 0x9853    66310 = 0x10306   71444 = 0x11714   71497 = 0x11749   
71511 = 0x11757   75120 = 0x12570   75121 = 0x12571   75122 = 0x12572   75123 = 0x12573   
75124 = 0x12574   75125 = 0x12575   75126 = 0x12576   75127 = 0x12577   75128 = 0x12578
75129 = 0x12579   75621 = 0x12765   86150 = 0x15086   88165 = 0x15865   91465 = 0x16549   
91769 = 0x16679   96617 = 0x17969   98711 = 0x18197   99481 = 0x18499

Nim

There are many ways to find the numbers. We chose to build directly the set of digits in base 10 and base 16 rather than using the string representations (more code but more efficient).

<lang Nim>import strutils, sugar

const Lim = 99_999

type Digit = 0..15

func digitSet(n: Natural; b: Positive): set[Digit] = 

 ## Return the set of digits of "n" written in base "b".
 assert b <= 16
 if n == 0: return {Digit 0}
 var n = n
 while n != 0:
   result.incl n mod b
   n = n div b
  1. Build the list of numbers.

let list = collect(newSeq): 

            for n in 0..Lim:
              if n.digitSet(10) == n.digitSet(16): n
  1. Display result.

echo "Found $1 numbers less than $2:".format(list.len, insertSep($(Lim + 1))) for i, n in list: 

 stdout.write ($n).align(5), if (i + 1) mod 10 == 0: '\n' else: ' '

echo()</lang>

Output:
Found 69 numbers less than 100_000:
    0     1     2     3     4     5     6     7     8     9
   53   371   913  1040  2080  2339  4100  5141  5412  5441
 6182  8200  9241 13593 13665 13969 16406 20530 26946 30979
32803 33638 33840 33841 33842 33843 33844 33845 33846 33847
33848 33849 34883 37943 38931 38966 38995 66310 71444 71497
71511 75120 75121 75122 75123 75124 75125 75126 75127 75128
75129 75621 86150 88165 91465 91769 96617 98711 99481

Phix

function handusc(integer n) return unique(sprintf("%x",n))=unique(sprintf("%d",n)) end function
?shorten(filter(tagset(100000,0),handusc),"found",10)
Output:
{0,1,2,3,4,5,6,7,8,9,"...",75128,75129,75621,86150,88165,91465,91769,96617,98711,99481," (69 found)"}

Quackery

<lang Quackery> [ 0 swap witheach [ bit | ] ] is ->set ( [ --> s ) 

 [ 10 base put
   dup  number$ ->set
   16 base replace
   swap number$ ->set
   base release
   = ]                         is dec=hex ( n --> b )

 []
 100000 times
   [ i^ dec=hex if
       [ i^ number$
         nested join ] ]
 60 wrap$</lang>
Output:
0 1 2 3 4 5 6 7 8 9 53 371 913 1040 2080 2339 4100
5141 5412 5441 6182 8200 9241 13593 13665 13969
16406 20530 26946 30979 32803 33638 33840 33841
33842 33843 33844 33845 33846 33847 33848 33849
34883 37943 38931 38966 38995 66310 71444 71497
71511 75120 75121 75122 75123 75124 75125 75126
75127 75128 75129 75621 86150 88165 91465 91769
96617 98711 99481

Raku

Much is left open to interpretation.

Numbers which when expressed in decimal and in hexadecimal are composed of the same digit glyphs. <lang perl6>say (^100000).hyper(:5000batch).grep( { [eqv] ($_, .fmt: '%x').map( *.comb.Bag ) } ).batch(10)».fmt('%5d').join("\n")</lang>

Output:
    0     1     2     3     4     5     6     7     8     9
   53   371   913  4100  5141  5412  6182  8200  9241 75120
75121 75122 75123 75124 75125 75126 75127 75128 75129 75621
86150 91465 98711 99481

Numbers which when expressed in decimal and in hexadecimal are composed from the same digit glyphs. <lang perl6>say (^100000).hyper(:5000batch).grep( { [eqv] ($_, .fmt: '%x').map( *.comb.Set ) } ).batch(10)».fmt('%5d').join("\n")</lang>

Output:
    0     1     2     3     4     5     6     7     8     9
   53   371   913  1040  2080  2339  4100  5141  5412  5441
 6182  8200  9241 13593 13665 13969 16406 20530 26946 30979
32803 33638 33840 33841 33842 33843 33844 33845 33846 33847
33848 33849 34883 37943 38931 38966 38995 66310 71444 71497
71511 75120 75121 75122 75123 75124 75125 75126 75127 75128
75129 75621 86150 88165 91465 91769 96617 98711 99481

REXX

<lang rexx>/*REXX pgm finds integers when shown in decimal and hexadecimal use the same numerals.*/ parse arg n cols . /*obtain optional argument from the CL.*/ if n== | n=="," then n = 100000 /*Not specified? Then use the default.*/ if cols== | cols=="," then cols= 10 /* " " " " " " */ w= 10 /*width of a number in any column. */ 

                    @hHex= ' decimal integers when displayed in decimal and'      ,
                           "hexadecimal use the same numerals, where  N  < "   commas(n)

say ' index │'center(@hHex, 1 + cols*(w+1) ) /*display the title for the output. */ say '───────┼'center("" , 1 + cols*(w+1), '─') /* " a sep " " " */ dHex= 0; idx= 1 /*initialize # of high hexadecimal nums*/ $= /*list of high hexadecimal #'s (so far)*/ 

   do j=0  for n;     h= d2x(j)                 /*search for high hexadecimal numbers. */
   if verify(j, h)>0  then iterate              /*Does the decimal and hexadecimal ··· */   /* ◄■■■■■■■■ a filter. */
   if verify(h, j)>0  then iterate              /*     ··· versions use same numerals? */   /* ◄■■■■■■■■ a filter. */
   dHex= dHex + 1                               /*bump number of decimal-hex numbers.  */
   $= $  right(commas(j), w)                    /*add a dec-hexadecimal number──► list.*/
   if dHex // cols \== 0          then iterate  /*have we populated a line of output?  */
   say center(idx, 7)'│'  substr($, 2);   $=    /*display what we have so far  (cols). */
   idx= idx + cols                              /*bump the  index  count for the output*/
   end   /*j*/

if $\== then say center(idx, 7)"│" substr($, 2) /*possible display residual output.*/ say '───────┴'center("" , 1 + cols*(w+1), '─') /*display the foot sep for output. */ say say 'Found ' commas(dHex) @hHex exit 0 /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ commas: parse arg ?; do jc=length(?)-3 to 1 by -3; ?=insert(',', ?, jc); end; return ?</lang>

output   when using the default inputs:
 index │     decimal integers when displayed in decimal and hexadecimal use the same numerals, where  N  <  100,000
───────┼───────────────────────────────────────────────────────────────────────────────────────────────────────────────
   1   │          0          1          2          3          4          5          6          7          8          9
  11   │         53        371        913      1,040      2,080      2,339      4,100      5,141      5,412      5,441
  21   │      6,182      8,200      9,241     13,593     13,665     13,969     16,406     20,530     26,946     30,979
  31   │     32,803     33,638     33,840     33,841     33,842     33,843     33,844     33,845     33,846     33,847
  41   │     33,848     33,849     34,883     37,943     38,931     38,966     38,995     66,310     71,444     71,497
  51   │     71,511     75,120     75,121     75,122     75,123     75,124     75,125     75,126     75,127     75,128
  61   │     75,129     75,621     86,150     88,165     91,465     91,769     96,617     98,711     99,481
───────┴───────────────────────────────────────────────────────────────────────────────────────────────────────────────

Found  69  decimal integers when displayed in decimal and hexadecimal use the same numerals, where  N  <  100,000

Ring

<lang ring> see "working..." + nl

row = 0 limit = 100000

for n = 0 to limit 

   flag1 = 1
   flag2 = 1
   decStr = string(n)
   hexStr = hex(n)
   for m = 1 to len(decStr)
       ind = substr(hexStr,decStr[m])
       if ind < 1
          flag1 = 0
          exit
       ok
   next
   for p = 1 to len(hexStr)
       ind = substr(decStr,hexStr[p])
       if ind < 1
          flag2 = 0
          exit
       ok
   next
   if flag1 = 1 and flag2 = 1
      row = row + 1
      see "" + n + " "
      if row%5 = 0
         see nl
      ok
   ok

next

see nl + "Found " + row + " numbers" + nl see "done..." + nl </lang>

Output:
working...
0 1 2 3 4 
5 6 7 8 9 
53 371 913 1040 2080 
2339 4100 5141 5412 5441 
6182 8200 9241 13593 13665 
13969 16406 20530 26946 30979 
32803 33638 33840 33841 33842 
33843 33844 33845 33846 33847 
33848 33849 34883 37943 38931 
38966 38995 66310 71444 71497 
71511 75120 75121 75122 75123 
75124 75125 75126 75127 75128 
75129 75621 86150 88165 91465 
91769 96617 98711 99481 
Found 69 numbers
done...

Wren

Library: Wren-fmt
Library: Wren-set

<lang ecmascript>import "/fmt" for Conv, Fmt import "/set" for Set

var limit = 1e5 var count = 0 System.print("Numbers under 100,000 which use the same digits in decimal or hex:") for (n in 0...limit) { 

   var h = Conv.hex(n)
   var hs = Set.new(h)
   var ns = Set.new(n.toString)
   if (hs == ns) {
       count = count + 1
       Fmt.write("$,6d ", n)
       if (count % 10 == 0) System.print()
   }

} System.print("\n\n%(count) such numbers found.")</lang>

Output:
Numbers under 100,000 which use the same digits in decimal or hex:
     0      1      2      3      4      5      6      7      8      9 
    53    371    913  1,040  2,080  2,339  4,100  5,141  5,412  5,441 
 6,182  8,200  9,241 13,593 13,665 13,969 16,406 20,530 26,946 30,979 
32,803 33,638 33,840 33,841 33,842 33,843 33,844 33,845 33,846 33,847 
33,848 33,849 34,883 37,943 38,931 38,966 38,995 66,310 71,444 71,497 
71,511 75,120 75,121 75,122 75,123 75,124 75,125 75,126 75,127 75,128 
75,129 75,621 86,150 88,165 91,465 91,769 96,617 98,711 99,481 

69 such numbers found.

XPL0

<lang XPL0>func DigitSet(N, D); \Return a bit array containing the set of digits in N divisible by D int N, D; int Set; [Set:= 0; repeat N:= N/D; 

       Set:= Set or 1<<rem(0);

until N=0; return Set; ];

int Count, N; [Count:= 0; for N:= 0 to 99999 do 

   [if DigitSet(N,10) = DigitSet(N,16) then
       [IntOut(0, N);
       Count:= Count+1;
       if rem(Count/10) = 0 then CrLf(0) else ChOut(0, 9\tab\);
       ];
   ];

CrLf(0); IntOut(0, Count); Text(0, " such numbers found. ") ]</lang>

Output:
0       1       2       3       4       5       6       7       8       9
53      371     913     1040    2080    2339    4100    5141    5412    5441
6182    8200    9241    13593   13665   13969   16406   20530   26946   30979
32803   33638   33840   33841   33842   33843   33844   33845   33846   33847
33848   33849   34883   37943   38931   38966   38995   66310   71444   71497
71511   75120   75121   75122   75123   75124   75125   75126   75127   75128
75129   75621   86150   88165   91465   91769   96617   98711   99481   
69 such numbers found.
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