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.

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

For example, the decimal number 2339 is 923 when written in hex. The set of digits used, ignoring order and duplicates, is {2, 3, 9} in both cases and hence this number satisfies the task requirements.

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

<lang Julia>using Combinatorics

dheq(N) = [i for i in 0:N for p in permutations(digits(i)) if evalpoly(16, reverse(p)) == i]

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

</lang>

Output:

0     1     2     3     4     5     6     7     8     9     
53    371   913   1040  1040  1041  1041  1042  1043  1044  
1044  1045  1046  1047  1048  1049  2080  2080  2081  2082  
2082  2083  2084  2085  2086  2087  2088  2088  2089  4100  
4100  5141  5141  5412  6182  8200  8200  9241  20530 20530 
21025 21025 26930 75120 75121 75121 75122 75122 75123 75124 
75125 75125 75126 75127 75127 75128 75129 75621 86150 91465 
98711 98711 99481 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)"}

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

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.