# Numbers with same digit set in base 10 and base 16

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.

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.

## 11l

Translation of: Python
```V col = 0
L(i) 100000
I Set(Array(String(i))) == Set(Array(hex(i)))
col++
print(‘#7’.format(i), end' "\n"[0 .< Int(col % 10 == 0)])
print()```
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
```

## ABC

```HOW TO RETURN base digitset n:
PUT {} IN set
WHILE n>0:
PUT n mod base IN digit
IF digit not.in set: INSERT digit IN set
PUT floor(n/base) IN n
RETURN set

PUT 0 IN col
FOR n IN {0..100000}:
IF 10 digitset n = 16 digitset n:
WRITE n>>8
PUT col+1 IN col
IF col mod 10 = 0: WRITE /```
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```

```with Ada.Text_Io;

procedure Same_Digits is

Columns : constant := 10;
Width   : constant := 8;

type Set_Type is array (0 .. 15) of Boolean;

function Digit_Set_Of (N : Natural; Base : Natural) return Set_Type is
Nn  : Natural  := N;
Set : Set_Type := (others => False);
begin
while Nn /= 0 loop
Set (Nn mod Base) := True;
Nn := Nn / Base;
end loop;
return Set;
end Digit_Set_Of;

package Natural_Io is new Ada.Text_Io.Integer_Io (Natural);

Count : Natural := 0;
begin
for N in 0 .. 99_999 loop
if Digit_Set_Of (N, Base => 10) = Digit_Set_Of (N, Base => 16) then
Count := Count + 1;
Put (N, Width => Width);
if Count mod Columns = 0 then
New_Line;
end if;
end if;
end loop;
New_Line;
Put ("Total numbers: "); Put (Count, Width => 3); New_Line;
end Same_Digits;
```
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
Total numbers:  69
```

## 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.

```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.```
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
```

## APL

Works with: Dyalog APL
```(⊢(/⍨)(≡/((⊂∘⍋⌷⊢)∘∪¨10 16(⊥⍣¯1)¨⊂))¨)0,⍳99999
```
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```

## AppleScript

```use AppleScript version "2.3.1" -- Mac OS X 10.9 (Mavericks) or later.
use sorter : script "Insertion sort" -- <https://www.rosettacode.org/wiki/Sorting_algorithms/Insertion_sort#AppleScript>

on sameDigitSetDecHex(n)
(* Integer number input assumed.
Numbers whose hex LSD > 9 are eliminated immediately. Ditto negatives.
Thereafter the hex form's tested first so that the dec form doesn't have to be if the hex is unsuitable. *)
tell n mod 16 to if ((it > 9) or (it < 0)) then return false

script o
on digitsOf(n, base)
set digits to {n mod base}
set n to n div base
repeat until (n = 0)
set d to n mod base
if (d > 9) then return false
if (d is not in digits) then set end of digits to d
set n to n div base
end repeat
tell sorter to sort(digits, 1, -1)

return digits
end digitsOf
end script

tell o's digitsOf(n, 16) to return ((it is not false) and (it = o's digitsOf(n, 10)))
end sameDigitSetDecHex

local output, n
set output to {}
repeat with n from 0 to 99999
if (sameDigitSetDecHex(n)) then set end of output to n
end repeat
return output
```
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}
```

## Arturo

```valid?: function [n][
equal? sort unique digits n
sort unique digits.base:16 n
]

print select 0..100000 => valid?
```
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`

## AWK

```# syntax: GAWK -f DECIMAL_-_HEXADECIMAL_NUMBERS.AWK
BEGIN {
start = 0
stop = 99999
for (i=start; i<=stop; i++) {
tmp = sprintf("%X",i)
leng_dec = length(i)
leng_hex = length(tmp)
hits_dec = hits_hex = 0
for (j=1; j<=leng_dec; j++) {
if (tmp ~ substr(i,j,1)) {
hits_dec++
}
}
if (leng_dec == hits_dec) {
for (j=1; j<=leng_hex; j++) {
if (i ~ substr(tmp,j,1)) {
hits_hex++
}
}
}
if (leng_hex == hits_hex) {
printf("%6d%1s",i,++count%10?"":"\n")
}
}
exit(0)
}
```
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
```

## C

```#include <stdio.h>
#define LIMIT 100000

int digitset(int num, int base) {
int set;
for (set = 0; num; num /= base)
set |= 1 << num % base;
return set;
}

int main() {
int i, c = 0;
for (i = 0; i < LIMIT; i++)
if (digitset(i,10) == digitset(i,16))
printf("%6d%c", i, ++c%10 ? ' ' : '\n');
printf("\n");
return 0;
}
```
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```

## C++

```#include <iostream>
#include <iomanip>
#include <bitset>

const int LIMIT = 100000;

std::bitset<16> digitset(int num, int base) {
std::bitset<16> set;
for (; num; num /= base) set.set(num % base);
return set;
}

int main() {
int c = 0;
for (int i=0; i<LIMIT; i++) {
if (digitset(i,10) == digitset(i,16)) {
std::cout << std::setw(7) << i;
if (++c % 10 == 0) std::cout << std::endl;
}
}
std::cout << std::endl;
return 0;
}
```
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```

## Cowgol

```include "cowgol.coh";

const LIMIT := 100000;

sub digitset(n: uint32, base: uint8): (set: uint16) is
var one: uint16 := 1;
set := 0;
while n != 0 loop
set := set | (one << (n % base as uint32) as uint8);
n := n / base as uint32;
end loop;
end sub;

var i: uint32 := 0;
var c: uint8 := 0;
while i < LIMIT loop
if digitset(i,10) == digitset(i,16) then
print_i32(i);
if c<9 then
c := c + 1;
print_char('\t');
else
c := 0;
print_nl();
end if;
end if;
i := i + 1;
end loop;
print_nl();```
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```

## Draco

```proc nonrec digitset(ulong n; byte b) word:
word set;
set := 0;
while n ~= 0 do
set := set | 1 << make(n % b, byte);
n := n / b
od;
set
corp

proc nonrec main() void:
ulong MAX = 100000;
ulong n;
byte col;
n := 0;
col := 0;
while n<MAX do
if digitset(n,10) = digitset(n,16) then
write(n:8);
col := col + 1;
if col % 10 = 0 then writeln() fi
fi;
n := n + 1;
od;
writeln()
corp```
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```

## Delphi

Works with: Delphi version 6.0

```function HasSameDigits1016(N: integer): boolean;
{Return true if base-10 string and base-16 string have same characters}
var S10,S16: string;
var I: integer;
begin
Result:=False;
{Get base-10 and -16 string}
S10:=IntToStr(N);
S16:=Format('%x',[N]);
{Compare S10 to S16}
for I:=1 to Length(S10) do
if Pos(S10[I],S16)=0 then exit;
{Compare S16 to S10}
for I:=1 to Length(S16) do
if Pos(S16[I],S10)=0 then exit;
Result:=True;
end;

procedure ShowSameDigits1016(Memo: TMemo);
var I,Cnt: integer;
var S: string;
begin
Cnt:=0;
for I:=0 to 100000-1 do
if HasSameDigits1016(I) then
begin
Inc(Cnt);
S:=S+Format('%8D',[I]);
If (Cnt mod 5)=0 then S:=S+CRLF;
end;
end;
```
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
Count=69
Elapsed Time: 41.373 ms.

```

## EasyLang

```func digset n b .
while n > 0
h = bitshift 1 (n mod b)
set = bitor set h
n = n div b
.
return set
.
for i = 0 to 100000 - 1
if digset i 10 = digset i 16
write i & " "
.
.```
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
```

## F#

```// Decimal-Hexdecimal: Nigel Galloway. June 7th., 2021
let rec fN g=function n when n<10->Some(Set.add n g)|n when n%16<10->fN(g.Add(n%16))(n/16) |_->None
let rec fG n g=match n/10,n%10 with (0,n)->Some(Set.add n g)|(n,i)->fG n (Set.add i g)
let g=Set.empty in seq{0..100000}|>Seq.filter(fun n->fN g n=fG n g)|>Seq.iter(printf "%d "); printfn ""
```
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
```

## Factor

Works with: Factor version 0.99 2021-02-05
```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
```
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
```

## FreeBASIC

```function is_sds( byval n as integer ) as boolean
dim as boolean in_dec(0 to 9), in_hex(0 to 9)
dim as integer nd = n, dh
while nd
in_dec( nd mod 10 ) = true
nd \= 10
wend
while n
dh = n mod 16
if dh > 9 then return false
in_hex( dh ) = true
n \= 16
wend
for i as uinteger = 0 to 9
if in_dec(i) <> in_hex(i) then return false
next i
return true
end function

dim as integer i, c=0

for i = 0 to 99999
if is_sds(i) then
print using "#####   ";i;
c+=1
if c mod 10 = 0 then print
end if
next i```
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

```

## Go

Translation of: Wren
```package main

import (
"fmt"
"rcu"
"strconv"
)

func equalSets(s1, s2 map[rune]bool) bool {
if len(s1) != len(s2) {
return false
}
for k, _ := range s1 {
_, ok := s2[k]
if !ok {
return false
}
}
return true
}

func main() {
const limit = 100_000
count := 0
fmt.Println("Numbers under 100,000 which use the same digits in decimal or hex:")
for n := 0; n < limit; n++ {
h := strconv.FormatInt(int64(n), 16)
hs := make(map[rune]bool)
for _, c := range h {
hs[c] = true
}
ns := make(map[rune]bool)
for _, c := range strconv.Itoa(n) {
ns[c] = true
}
if equalSets(hs, ns) {
count++
fmt.Printf("%6s ", rcu.Commatize(n))
if count%10 == 0 {
fmt.Println()
}
}
}
fmt.Printf("\n\n%d such numbers found.\n", count)
}
```
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.
```

```import qualified Data.Set as S
import Numeric (showHex)

---- NUMBERS WITH THE SAME DIGIT SET IN DECIMAL AND HEX --

sameDigitSet :: (Integral a, Show a) => a -> [(a, String)]
sameDigitSet n =
[ (n, h)
| let h = showHex n "",
S.fromList h == S.fromList (show n)
]

--------------------------- TEST -------------------------
main = do
print ("decimal", "hex")
mapM_ print \$ [0 .. 100000] >>= sameDigitSet
```
Output:
```("decimal","hex")
(0,"0")
(1,"1")
(2,"2")
(3,"3")
(4,"4")
(5,"5")
(6,"6")
(7,"7")
(8,"8")
(9,"9")
(53,"35")
(371,"173")
(913,"391")
(1040,"410")
(2080,"820")
(2339,"923")
(4100,"1004")
(5141,"1415")
(5412,"1524")
(5441,"1541")
(6182,"1826")
(8200,"2008")
(9241,"2419")
(13593,"3519")
(13665,"3561")
(13969,"3691")
(16406,"4016")
(20530,"5032")
(26946,"6942")
(30979,"7903")
(32803,"8023")
(33638,"8366")
(33840,"8430")
(33841,"8431")
(33842,"8432")
(33843,"8433")
(33844,"8434")
(33845,"8435")
(33846,"8436")
(33847,"8437")
(33848,"8438")
(33849,"8439")
(34883,"8843")
(37943,"9437")
(38931,"9813")
(38966,"9836")
(38995,"9853")
(66310,"10306")
(71444,"11714")
(71497,"11749")
(71511,"11757")
(75120,"12570")
(75121,"12571")
(75122,"12572")
(75123,"12573")
(75124,"12574")
(75125,"12575")
(75126,"12576")
(75127,"12577")
(75128,"12578")
(75129,"12579")
(75621,"12765")
(86150,"15086")
(88165,"15865")
(91465,"16549")
(91769,"16679")
(96617,"17969")
(98711,"18197")
(99481,"18499")```

## J

Decimal numbers on left:

```   require'convert'
(":,.' ',.;@hfd"1),.I.(": -:&~.&(/:~) hfd)"0 i.1e5
0 0
1 1
2 2
3 3
4 4
5 5
6 6
7 7
8 8
9 9
53 35
371 173
913 391
1040 410
2080 820
2339 923
4100 1004
5141 1415
5412 1524
5441 1541
6182 1826
8200 2008
9241 2419
13593 3519
13665 3561
13969 3691
16406 4016
20530 5032
26946 6942
30979 7903
32803 8023
33638 8366
33840 8430
33841 8431
33842 8432
33843 8433
33844 8434
33845 8435
33846 8436
33847 8437
33848 8438
33849 8439
34883 8843
37943 9437
38931 9813
38966 9836
38995 9853
66310 10306
71444 11714
71497 11749
71511 11757
75120 12570
75121 12571
75122 12572
75123 12573
75124 12574
75125 12575
75126 12576
75127 12577
75128 12578
75129 12579
75621 12765
86150 15086
88165 15865
91465 16549
91769 16679
96617 17969
98711 18197
99481 18499
```

## JavaScript

```(() => {
"use strict";

const main = () => [
"(dec, hex)",
...enumFromTo(1)(100000).flatMap(n => {
const
d = n.toString(10),
h = n.toString(16);

return eqSet(new Set(d))(
new Set(h)
) ? [
`(\${d}, \${h})`
] : [];
})
].join("\n");

// --------------------- GENERIC ---------------------

// enumFromTo :: Int -> Int -> [Int]
const enumFromTo = m =>
n => Array.from({
length: 1 + n - m
}, (_, i) => m + i);

// eqSet :: Set a -> Set a -> Bool
const eqSet = a =>
// True if the two sets have
// the same size and members.
b => a.size === b.size && (
Array.from(a).every(x => b.has(x))
);

// MAIN ---
return main();
})();
```
Output:
```(dec, hex)
(1, 1)
(2, 2)
(3, 3)
(4, 4)
(5, 5)
(6, 6)
(7, 7)
(8, 8)
(9, 9)
(53, 35)
(371, 173)
(913, 391)
(1040, 410)
(2080, 820)
(2339, 923)
(4100, 1004)
(5141, 1415)
(5412, 1524)
(5441, 1541)
(6182, 1826)
(8200, 2008)
(9241, 2419)
(13593, 3519)
(13665, 3561)
(13969, 3691)
(16406, 4016)
(20530, 5032)
(26946, 6942)
(30979, 7903)
(32803, 8023)
(33638, 8366)
(33840, 8430)
(33841, 8431)
(33842, 8432)
(33843, 8433)
(33844, 8434)
(33845, 8435)
(33846, 8436)
(33847, 8437)
(33848, 8438)
(33849, 8439)
(34883, 8843)
(37943, 9437)
(38931, 9813)
(38966, 9836)
(38995, 9853)
(66310, 10306)
(71444, 11714)
(71497, 11749)
(71511, 11757)
(75120, 12570)
(75121, 12571)
(75122, 12572)
(75123, 12573)
(75124, 12574)
(75125, 12575)
(75126, 12576)
(75127, 12577)
(75128, 12578)
(75129, 12579)
(75621, 12765)
(86150, 15086)
(88165, 15865)
(91465, 16549)
(91769, 16679)
(96617, 17969)
(98711, 18197)
(99481, 18499)```

## jq

Works with: jq

Also works with gojq, the Go implementation of jq.

Also works with fq, a Go implementation of a large subset of jq

```# The def of _nwise/1 is included here in case gojq or fq is used.
def _nwise(\$n):
def nw: if length <= \$n then . else .[0:\$n] , (.[\$n:] | nw) end;
nw;

def chars: explode[] | [.] | implode;

# decimal number to hex string using lower-case letters
def hex:
def stream:
recurse(if . > 0 then ./16|floor else empty end) | . % 16 ;
if . == 0 then "0"
else [stream] | reverse | .[1:]
|  map(if . < 10 then 48 + . else . + 87 end) | implode
end;

def lpad(\$len): tostring | (\$len - length) as \$l | (" " * \$l)[:\$l] + .;

# Emit a stream of same-digit numbers, up to .
def u: [tostring|chars] | unique;
range(0; .) | select((hex|u) == u);

1e5
| "Numbers under \(.) which use the same digits in decimal as in hex:",
| ((_nwise(10) | join(" ")),
"\n\(length) such numbers found." ) )```
Output:
```Numbers under 100000 which use the same digits in decimal as in hex:
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.
```

## Julia

```dhstring(N) = [i for i in 0:N if sort(unique(digits(i))) == sort(unique(digits(i, base=16)))]

foreach(p -> print(rpad(p[2], 6), p[1] % 10 == 0 ? "\n" : ""), enumerate(dhstring(100000)))
```
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
```

## langur

Translation of: Python
```# using hash keys to create a pseudo-set
val makeset = fn n:foldfrom(fn h, v: h ~ {v: 0}, {:}, split(n))

var col = 1
for n in 0..99999 {
if makeset(n) == makeset(string(n, 16)) {
write "{{n:7}}"
if col div 10: writeln()
col += 1
}
}
writeln()```
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
```

## Mathematica/Wolfram Language

```ClearAll[Base1016SameDigitsQ]
Base1016SameDigitsQ[n_Integer] := Module[{id10, id16},
id10 = Union[IntegerDigits[n, 10]];
id16 = Union[IntegerDigits[n, 16]];
id10 === id16
]
Multicolumn[Select[Range[0, 10^5 - 1], Base1016SameDigitsQ], Appearance -> "Horizontal"]
```
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
```

## 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).

```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

# Build the list of numbers.
let list = collect(newSeq):
for n in 0..Lim:
if n.digitSet(10) == n.digitSet(16): n

# 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()
```
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 ```

## OCaml

```module CSet = Set.Make(struct
type t = char
let compare = compare
end)

let str2cset str = CSet.add_seq (String.to_seq str) CSet.empty

let has_same_digits n =
let deci = Format.sprintf "%d" n in
let hexa = Format.sprintf "%x" n in
(* Don't use '=' to compare sets, it only returns true
for sets that are structurally the same, (same elements added in same order)
use CSet.equal to check they have the same elements *)
CSet.equal (str2cset deci) (str2cset hexa)

let rec list_similar ?(acc=[]) n =
if n < 0 then acc
else if has_same_digits n then list_similar ~acc:(n::acc) (n-1)
else list_similar ~acc (n-1)

let () =
let same_digits = list_similar 100_000 in
List.iteri (fun i x ->
Format.printf "%6d:%#8x%s" x x (if i mod 6 = 5 then "\n" else "  ")) same_digits;
print_newline ()
```
Output:
```     0:       0       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 ```

## Pascal

simply adding 1 to a number and convert as if hex digits.

```program Dec_Hex_same_UsedDigits;
{\$IFDEF FPC}
{\$MODE DELPHI}  {\$OPTIMIZATION ON,ALL}  {\$COPERATORS ON}
{\$ELSE}
{\$APPTYPE CONSOLE}
{\$ENDIF}
const
UpperLimit =  100*1000;//1000*1000*1000
type
tUsedDigits = array[0..15] of byte;
var
FormCnt: Int32;
UsedDigits : tUsedDigits;

procedure Out_(n,h:Uint32);
Begin
write(n:11,':',h:7);
inc(FormCnt);
If FormCnt >= 4 then
Begin
FormCnt := 0;
writeln;
end;
end;

function DecHexToDec(n:Uint32):UInt32;
//convert n as its decimal digits are a hex number
//marking used Digits
var
pD : pUint64;
q,r,pot16 : UInt32;
begin
//clear UsedDigits
//For q := Low(UsedDigits) to High(UsedDigits) do  UsedDigits[q] := 0;
//much faster
pD := @UsedDigits;pD[0]:= 0;pD[1]:= 0;

result := 0;
pot16 := 0;
repeat
q := n Div 10;
r := n - 10* q;//n mod 10
//marked by hex
UsedDigits[r] := 2;
result := result+ r shl pot16;
inc(pot16,4);
n := q;
until n = 0;
end;

var
DecHex,n:Uint32;
i,q,r,count : Uint32;
Begin
FormCnt := 0;
count := 0;
DecHex := 0;
repeat
n := DecHexToDec(DecHex);
if n > UpperLimit then
break;
//check UsedDigits
i := n;
repeat
q := i Div 10;
r := i - 10* q;
//if unused digit then break
if UsedDigits[r] = 0 then
BREAK;
//marked by dec
UsedDigits[r] := 1;
i := q;
until i = 0;
if i = 0 then
Begin
repeat
//was marked only by hex
if UsedDigits[i]>1 then
break;
inc(i);
until i > 9;
if i > 9 then
Begin
if n< 100*1000 then
Out_(n,DecHex);
inc(count);
end;
end;
inc(DecHex);
until false;
writeln;
writeln('count : ',count);
END.
```
Output:
```TIO.RUN
0:     0        1:     1        2:     2        3:     3
4:     4        5:     5        6:     6        7:     7
8:     8        9:     9       53:    35      371:   173
913:   391     1040:   410     2080:   820     2339:   923
4100:  1004     5141:  1415     5412:  1524     5441:  1541
6182:  1826     8200:  2008     9241:  2419    13593:  3519
13665:  3561    13969:  3691    16406:  4016    20530:  5032
26946:  6942    30979:  7903    32803:  8023    33638:  8366
33840:  8430    33841:  8431    33842:  8432    33843:  8433
33844:  8434    33845:  8435    33846:  8436    33847:  8437
33848:  8438    33849:  8439    34883:  8843    37943:  9437
38931:  9813    38966:  9836    38995:  9853    66310: 10306
71444: 11714    71497: 11749    71511: 11757    75120: 12570
75121: 12571    75122: 12572    75123: 12573    75124: 12574
75125: 12575    75126: 12576    75127: 12577    75128: 12578
75129: 12579    75621: 12765    86150: 15086    88165: 15865
91465: 16549    91769: 16679    96617: 17969    98711: 18197
99481: 18499
count : 69
//1000*1000*1000
966366598:39999586  966366853:39999685
count : 54558 Real time: 1.666 s```

## Perl

```use strict;
no warnings;
use feature 'say';

sub eqv { (join '', sort split '', \$_[0]) eq (join '', sort split '', \$_[1]) }
say join ' ', grep { eqv \$_, sprintf '%x', \$_ } 1..100_000;
```
Output:
`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`

## 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)"}
```

## Python

### Procedural

```col = 0
for i in range(100000):
if set(str(i)) == set(hex(i)[2:]):
col += 1
print("{:7}".format(i), end='\n'[:col % 10 == 0])
print()
```
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```

### Functional

```'''Decimal - Hexadecimal numbers'''

# p :: Int -> Bool
def p(n):
'''True if the hex and dec representations
of n use the same set of digits.
'''
return set(hex(n)[2:]) == set(str(n))

# ------------------------- TEST -------------------------
# main :: IO ()
def main():
'''Matches below 100000'''
print(
table(10)([
str(x) for x in range(100000)
if p(x)
])
)

# ----------------------- GENERIC ------------------------

# chunksOf :: Int -> [a] -> [[a]]
def chunksOf(n):
'''A series of lists of length n, subdividing the
contents of xs. Where the length of xs is not evenly
divisible, the final list will be shorter than n.
'''
def go(xs):
return (
xs[i:n + i] for i in range(0, len(xs), n)
) if 0 < n else None
return go

# table :: Int -> [a] -> String
def table(n):
'''A list of values formatted as
right-justified rows of n columns.
'''
def go(xs):
w = len(xs[-1])
return '\n'.join(
' '.join(row) for row in chunksOf(n)([
x.rjust(w, ' ') for x in xs
])
)
return go

# MAIN ---
if __name__ == '__main__':
main()
```
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```

or in terms of a list comprehension:

```for nh in ([
(n, h) for n in range(0, 1 + 100000)
if (
(h := hex(n)[2:])
and set(str(n)) == set(h)
)
]):
print(nh)
```
```(0, '0')
(1, '1')
(2, '2')
(3, '3')
(4, '4')
(5, '5')
(6, '6')
(7, '7')
(8, '8')
(9, '9')
(53, '35')
(371, '173')
(913, '391')
(1040, '410')
(2080, '820')
(2339, '923')
(4100, '1004')
(5141, '1415')
(5412, '1524')
(5441, '1541')
(6182, '1826')
(8200, '2008')
(9241, '2419')
(13593, '3519')
(13665, '3561')
(13969, '3691')
(16406, '4016')
(20530, '5032')
(26946, '6942')
(30979, '7903')
(32803, '8023')
(33638, '8366')
(33840, '8430')
(33841, '8431')
(33842, '8432')
(33843, '8433')
(33844, '8434')
(33845, '8435')
(33846, '8436')
(33847, '8437')
(33848, '8438')
(33849, '8439')
(34883, '8843')
(37943, '9437')
(38931, '9813')
(38966, '9836')
(38995, '9853')
(66310, '10306')
(71444, '11714')
(71497, '11749')
(71511, '11757')
(75120, '12570')
(75121, '12571')
(75122, '12572')
(75123, '12573')
(75124, '12574')
(75125, '12575')
(75126, '12576')
(75127, '12577')
(75128, '12578')
(75129, '12579')
(75621, '12765')
(86150, '15086')
(88165, '15865')
(91465, '16549')
(91769, '16679')
(96617, '17969')
(98711, '18197')
(99481, '18499')```

## 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\$```
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

Only bother to check numbers that could possibly match.

Several different interpretations of the (originally very vague) task instructions. It has now been clarified to mean the second.

```say "Numbers up to 100,000 which when expressed in hexadecimal and in decimal
are composed of the same digit glyphs. (All the same glyphs, all the same
quantity.)\n";
display-numbers calculated-with &infix:<eqv>, <Bag>;

say "\nNumbers up to 100,000 which when expressed in hexadecimal and in decimal
are composed from the same digit glyphs. (All the same glyphs  are present,
possibly different quantity.)\n";
display-numbers calculated-with &infix:<eqv>, <Set>;

say "\nNumbers up to 100,000 which, when expressed in hexadecimal use glyphs
that are a subset of those used when expressed in decimal. (Every glyph in
decimal is present in hexadecimal the same or fewer (possibly zero) times)\n";
display-numbers calculated-with &infix:<⊆>, <Bag>;

say "\nNumbers up to 100,000 which, when expressed in hexadecimal use glyphs
that are a subset of those used when expressed in decimal. (Every glyph in
decimal is present in hexadecimal in some quantity, possibly zero, possibly more
than in decimal)\n";
display-numbers calculated-with &infix:<⊆>, <Set>;

sub display-numbers (\$_) { say .elems ~ " found:\n" ~ .batch(20)».fmt('%5d').join: "\n" }

sub calculated-with ( &op, \$container ) {
cache ^18699 .map( {:16(.Str)} ).hyper(:1000batch).grep( {
reduce( &op, (.fmt('%x'), \$_).map: { .comb."\$container"() } )
} )
}
```
Output:
```Numbers which when expressed in hexadecimal and in decimal are composed of
the same digit glyphs. (All the same glyphs, all the same quantity.)

34 found:
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 hexadecimal and in decimal are composed
from the same digit glyphs. (All the same glyphs are present, possibly
different quantity.)

69 found:
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

Numbers which, when expressed in hexadecimal use glyphs that are a subset
of those used when expressed in decimal. (Every glyph in decimal is present in
hexadecimal the same or fewer (possibly zero) times)

141 found:
0     1     2     3     4     5     6     7     8     9    53   371   913  1040  1041  1042  1043  1044  1045  1046
1047  1048  1049  1345  1937  2080  2081  2082  2083  2084  2085  2086  2087  2088  2089  2339  4100  5141  5412  6182
8200  9241 12306 13593 13665 13969 16400 16401 16402 16403 16404 16405 16406 16407 16408 16409 16743 18453 20513 20530
20546 21025 25169 25896 25986 26370 26738 26913 26930 26946 29217 29714 30768 30784 30979 32800 32801 32802 32803 32804
32805 32806 32807 32808 32809 32850 33589 33840 33841 33842 33843 33844 33845 33846 33847 33848 33849 34868 34880 34881
34882 34883 34884 34885 34886 34887 34888 34889 36902 36950 37492 37943 38931 38960 38961 38962 38963 38964 38965 38966
38967 38968 38969 38984 38995 39298 75120 75121 75122 75123 75124 75125 75126 75127 75128 75129 75621 86150 91465 98711
99481

Numbers which, when expressed in hexadecimal use glyphs that are a subset
of those used when expressed in decimal. (Every glyph in decimal is present in
hexadecimal in some quantity, possibly zero, possibly more than in decimal)

514 found:
0     1     2     3     4     5     6     7     8     9    17    53    85   371   853   913  1024  1040  1041  1042
1043  1044  1045  1046  1047  1048  1049  1345  1365  1604  1633  1635  1638  1689  1937  2048  2080  2081  2082  2083
2084  2085  2086  2087  2088  2089  2178  2184  2339  4100  4160  4371  4417  4471  4481  4721  4913  4931  5140  5141
5412  5441  5461  6168  6182  8200  8210  8320  8721  9241  9284  9523  9625  9762  9826  9862 10248 10258 10280 10529
12304 12305 12306 12307 12320 12340 12563 12593 12643 12803 12833 12834 12835 12853 12953 13056 13057 13059 13062 13072
13073 13075 13079 13080 13104 13105 13107 13124 13171 13175 13185 13187 13209 13364 13384 13427 13448 13459 13585 13587
13589 13593 13651 13653 13654 13665 13846 13862 13926 13969 14385 14387 14388 14739 16400 16401 16402 16403 16404 16405
16406 16407 16408 16409 16420 16480 16640 16704 16740 16742 16743 17408 17409 17425 17426 17428 17431 17442 17463 17473
17476 17479 17480 17495 17524 17745 18247 18440 18449 18452 18453 18456 18472 18483 18497 18504 18564 20485 20501 20512
20513 20514 20517 20530 20531 20533 20544 20546 20548 20549 20560 20561 20562 20563 20564 20565 20566 20567 20568 20569
20576 20597 21025 21395 21504 21524 21540 21541 21845 21905 22357 22568 22658 24608 24610 24630 24640 24680 25106 25126
25169 25186 25361 25604 25634 25684 25896 25961 25986 26129 26130 26131 26134 26145 26146 26148 26150 26163 26184 26208
26210 26214 26248 26370 26407 26470 26471 26487 26658 26728 26738 26758 26913 26914 26918 26921 26930 26931 26934 26937
26946 26948 26965 26978 26982 26984 26985 28704 28706 28740 28807 29217 29337 29714 29764 29847 30467 30471 30517 30547
30567 30576 30579 30728 30768 30784 30976 30979 31097 32800 32801 32802 32803 32804 32805 32806 32807 32808 32809 32840
32850 33280 33587 33589 33638 33689 33840 33841 33842 33843 33844 33845 33846 33847 33848 33849 33864 34678 34820 34852
34867 34868 34871 34872 34880 34881 34882 34883 34884 34885 34886 34887 34888 34889 34948 34968 36902 36950 36960 37139
37169 37492 37529 37689 37779 37924 37940 37943 37945 38195 38791 38792 38793 38920 38931 38952 38960 38961 38962 38963
38964 38965 38966 38967 38968 38969 38984 38995 39048 39185 39187 39193 39200 39201 39202 39203 39204 39205 39206 39207
39208 39209 39217 39218 39219 39225 39234 39241 39250 39251 39253 39257 39266 39267 39287 39298 39313 39315 39321 66310
67140 67190 69910 69913 69921 70001 70162 70513 71025 71206 71265 71266 71286 71440 71441 71442 71443 71444 71445 71446
71447 71448 71449 71462 71473 71489 71492 71495 71497 71504 71505 71509 71511 71526 71537 71539 71540 71541 71543 71569
71680 71748 71800 71808 71809 71815 71816 71940 71953 71957 71959 71961 71993 74129 75120 75121 75122 75123 75124 75125
75126 75127 75128 75129 75621 76129 78103 78131 78135 78136 78193 79153 79731 81940 82194 82241 82471 82514 84100 84104
86150 87315 87351 87415 88145 88152 88165 90163 91465 91665 91670 91671 91673 91682 91760 91761 91762 91763 91764 91765
91766 91767 91768 91769 92561 94617 95761 96017 96617 98581 98711 98712 98713 99481```

## 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.  */
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 ?
```
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

```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```
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...
```

## RPL

Works with: HP version 49
```« → b
« #0
WHILE OVER REPEAT
SWAP b IDIV2
ROT SWAP ALOG R→B OR
END NIP
» » 'DIGSET' STO

« { }
0 99999 FOR n
IF n 10 DIGSET n 16 DIGSET == THEN n + END
NEXT
```
Output:
```1: { 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 }
```

## Ruby

```p (1..100_000).select{|n| n.digits.to_set == n.digits(16).to_set}
```
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]
```

## SETL

```program Numbers_with_same_digit_set_in_base_10_and_base_16;
loop for i in [0..100000] | digitset(i,10) = digitset(i,16) do
if (col +:= 1) mod 10 = 0 then print; end if;
end loop;
print;

proc digitset(n, b);
s := {};
loop until n=0 do
s with:= n mod b;
n div:= b;
end loop;
return s;
end proc;
end program;```
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```

## Sidef

Simple solution:

```^1e5 -> grep { Set(.digits...) == Set(.digits(16)...) }.say
```

Recursively generate the numbers (2x faster):

```func generate_from_prefix(limit, p, base, digits) {

var seq = [p]

for d in (digits) {
var t = [d, p...]
if (t.digits2num(base) <= limit) {
seq << __FUNC__(limit, t, base, digits)...
}
}

return seq
}

func numbers_with_same_digitset(limit, base = 10) {

(1..9).map  {|p| generate_from_prefix(limit, [p], base, @(0..9))... }\
.map  {|t| digits2num(t, base) }\
.grep {|t| Set(t.digits...) == Set(t.digits(base)...) }\
.sort\
.prepend(0)
}

say numbers_with_same_digitset(1e5, 16)
```
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]
```

## Wren

Library: Wren-fmt
Library: Wren-set
```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.")
```
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

```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.
")
]```
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.
```

## Zig

Translation of: C
```const print = @import("std").debug.print;
fn digitset(numinp: u32, base: u32) u32 {
var set: u32 = 0;
var num: u32 = numinp;
while (num != 0) : (num /= base) {
set |= @as(u32, 1) << @truncate(u5, num % base);
}
return set;
}
pub fn main() void {
var i: u32 = 0;
const LIMIT: u32 = 100000;
while (i < LIMIT) : (i += 1) {
if (digitset(i, 10) == digitset(i, 16)) {
print("{}\n", .{i});
}
}
}
```