Smallest Diversifying Exponent

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A pandigital number is one which contains every digit from 0 to 9 at least once. 1234567890, 1902837465000000, and 9023289761326634265 are all pandigital.

A diverse pair of numbers is a pair of numbers $(a, b)$ such that $a^b$ is pandigital. $b$ is called the diversifying exponent.

Challenge: Given a number $a$, find the smallest corresponding diversifying exponent $b$. This is a code-golf, so the shortest program in bytes wins.

(You may assume that there exists such an exponent, that is, your program will not be given invalid input, such as a power of 10.)

Your solution must be able to handle at the minimum the given test cases, but it should theoretically handle all valid inputs.

This is A090493 on OEIS.

Test cases

2 -> 68

3 -> 39

4 -> 34

5 -> 19

6 -> 20

7 -> 18

8 -> 28

9 -> 24

11 -> 23

12 -> 22

13 -> 22

14 -> 21

15 -> 12

16 -> 17

17 -> 14

18 -> 21

19 -> 17

20 -> 51

21 -> 17

22 -> 18

23 -> 14

24 -> 19

25 -> 11

26 -> 18

27 -> 13

28 -> 11

29 -> 12

30 -> 39

31 -> 11

32 -> 14

33 -> 16

34 -> 14

35 -> 19

36 -> 10

asked 2 hours ago

Conor O'Brien

29k263160

1

I want to point out a special case 1234567890 -> 1.
– Bubbler
2 hours ago

add a comment |

up vote
4
down vote

favorite

A pandigital number is one which contains every digit from 0 to 9 at least once. 1234567890, 1902837465000000, and 9023289761326634265 are all pandigital.

A diverse pair of numbers is a pair of numbers $(a, b)$ such that $a^b$ is pandigital. $b$ is called the diversifying exponent.

Challenge: Given a number $a$, find the smallest corresponding diversifying exponent $b$. This is a code-golf, so the shortest program in bytes wins.

(You may assume that there exists such an exponent, that is, your program will not be given invalid input, such as a power of 10.)

Your solution must be able to handle at the minimum the given test cases, but it should theoretically handle all valid inputs.

This is A090493 on OEIS.

Test cases

2 -> 68

3 -> 39

4 -> 34

5 -> 19

6 -> 20

7 -> 18

8 -> 28

9 -> 24

11 -> 23

12 -> 22

13 -> 22

14 -> 21

15 -> 12

16 -> 17

17 -> 14

18 -> 21

19 -> 17

20 -> 51

21 -> 17

22 -> 18

23 -> 14

24 -> 19

25 -> 11

26 -> 18

27 -> 13

28 -> 11

29 -> 12

30 -> 39

31 -> 11

32 -> 14

33 -> 16

34 -> 14

35 -> 19

36 -> 10

asked 2 hours ago

Conor O'Brien

29k263160

1

I want to point out a special case 1234567890 -> 1.
– Bubbler
2 hours ago

add a comment |

up vote
4
down vote

favorite

A pandigital number is one which contains every digit from 0 to 9 at least once. 1234567890, 1902837465000000, and 9023289761326634265 are all pandigital.

A diverse pair of numbers is a pair of numbers $(a, b)$ such that $a^b$ is pandigital. $b$ is called the diversifying exponent.

Challenge: Given a number $a$, find the smallest corresponding diversifying exponent $b$. This is a code-golf, so the shortest program in bytes wins.

(You may assume that there exists such an exponent, that is, your program will not be given invalid input, such as a power of 10.)

Your solution must be able to handle at the minimum the given test cases, but it should theoretically handle all valid inputs.

This is A090493 on OEIS.

Test cases

2 -> 68

3 -> 39

4 -> 34

5 -> 19

6 -> 20

7 -> 18

8 -> 28

9 -> 24

11 -> 23

12 -> 22

13 -> 22

14 -> 21

15 -> 12

16 -> 17

17 -> 14

18 -> 21

19 -> 17

20 -> 51

21 -> 17

22 -> 18

23 -> 14

24 -> 19

25 -> 11

26 -> 18

27 -> 13

28 -> 11

29 -> 12

30 -> 39

31 -> 11

32 -> 14

33 -> 16

34 -> 14

35 -> 19

36 -> 10

asked 2 hours ago

Conor O'Brien

29k263160

A pandigital number is one which contains every digit from 0 to 9 at least once. 1234567890, 1902837465000000, and 9023289761326634265 are all pandigital.

A diverse pair of numbers is a pair of numbers $(a, b)$ such that $a^b$ is pandigital. $b$ is called the diversifying exponent.

Challenge: Given a number $a$, find the smallest corresponding diversifying exponent $b$. This is a code-golf, so the shortest program in bytes wins.

(You may assume that there exists such an exponent, that is, your program will not be given invalid input, such as a power of 10.)

Your solution must be able to handle at the minimum the given test cases, but it should theoretically handle all valid inputs.

This is A090493 on OEIS.

Test cases

2 -> 68

3 -> 39

4 -> 34

5 -> 19

6 -> 20

7 -> 18

8 -> 28

9 -> 24

11 -> 23

12 -> 22

13 -> 22

14 -> 21

15 -> 12

16 -> 17

17 -> 14

18 -> 21

19 -> 17

20 -> 51

21 -> 17

22 -> 18

23 -> 14

24 -> 19

25 -> 11

26 -> 18

27 -> 13

28 -> 11

29 -> 12

30 -> 39

31 -> 11

32 -> 14

33 -> 16

34 -> 14

35 -> 19

36 -> 10

code-golf math

asked 2 hours ago

Conor O'Brien

29k263160

asked 2 hours ago

Conor O'Brien

29k263160

asked 2 hours ago

Conor O'Brien

29k263160

asked 2 hours ago

Conor O'Brien

29k263160

asked 2 hours ago

Conor O'Brien

29k263160

1

I want to point out a special case 1234567890 -> 1.
– Bubbler
2 hours ago

add a comment |

1

I want to point out a special case 1234567890 -> 1.
– Bubbler
2 hours ago

I want to point out a special case 1234567890 -> 1.
– Bubbler
2 hours ago

add a comment |

5 Answers
5

active

oldest

votes

up vote
2
down vote

JavaScript (Node.js), 51 46 43 bytes

Takes input as a BigInt literal. Returns true instead of 1.

f=(n,k=n)=>new Set(n+'').size>9||1+f(n*k,k)

Try it online!

edited 1 hour ago

answered 2 hours ago

Arnauld

71.9k688301

1

I keep forgetting JS has bigint's now :D
– Conor O'Brien
2 hours ago

I am slightly dubious regarding returning true instead of 1. That doesn't seem to match anything described at codegolf.meta.stackexchange.com/questions/9263/…
– Sparr
1 hour ago

2

@Sparr Here is the current consensus.
– Arnauld
1 hour ago

Thanks. I put a new Answer on my link referring to that.
– Sparr
46 mins ago

add a comment |

up vote
0
down vote

J, 25 bytes

>:@]^:(10>#@~.@":@^)^:_&1

Try it online!

Single monadic verb. The input should be an extended-precision integer (e.g. 2x).

How it works

>:@]^:(10>#@~.@":@^)^:_&1    Monadic verb. Input: base a

    ^:              ^:_      Good old do-while loop.

                       &1    Given 1 as the starting point for b,

>:@]                         increment it each step

      (            )         and continue while the condition is true:

               ":@^          Digits of a^b

            ~.@              Unique digits

          #@                 Count of unique digits

       10>                   is less than 10

answered 2 hours ago

Bubbler

6,204759

add a comment |

up vote
0
down vote

Jelly, 12 11 bytes

1*@ṾØDfƑʋ1#

Try it online!

How it works

1*@ṾØDfƑʋ1#  Main link. Argument: n



1            Set the return value to 1.

         1#  Call the link to the left for k = 1, 2, ... and with right argument n,

             until it returns a truthy value.

        ʋ      Combine the four links to the left into a dyadic chain.

 *@              Compute n**k.

   Ṿ             Convert it to its string representation.

    ØD           Yield "0123456789".

      fƑ         Filter and return 1 is the result is equal to the left argument.

edited 1 hour ago

answered 1 hour ago

Dennis♦

186k32295735

add a comment |

up vote
0
down vote

Perl 6, 32 bytes

{first ($_** *).comb.Set>9,1..*}

Try it online!

Pretty self-explanatory.

Explanation

{                              }  # Anonymous code block

first                     ,1..*   # First positive number that

      ($_** *)    # When the input is raised to that power

              .comb.Set    # The set of digits

                       >9  # Is longer than 9

edited 56 mins ago

answered 2 hours ago

Jo King

20.5k246108

add a comment |

up vote
0
down vote

Python 2, 44 bytes

f=lambda n,k=1:11>len(set(`k`))and-~f(n,n*k)

Input has to be a long, as `k` behaves differently for longs and ints.

Try it online!

answered 38 mins ago

Dennis♦

186k32295735

add a comment |

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…Try to optimize your score. For instance, answers to code-golf challenges should attempt to be as short as possible. You can always include a readable version of the code in addition to the competitive one.
Explanations of your answer make it more interesting to read and are very much encouraged.

…Include a short header which indicates the language(s) of your code and its score, as defined by the challenge.

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5 Answers
5

active

oldest

votes

5 Answers
5

active

oldest

votes

up vote
2
down vote

JavaScript (Node.js), 51 46 43 bytes

Takes input as a BigInt literal. Returns true instead of 1.

f=(n,k=n)=>new Set(n+'').size>9||1+f(n*k,k)

Try it online!

edited 1 hour ago

answered 2 hours ago

Arnauld

71.9k688301

1

I keep forgetting JS has bigint's now :D
– Conor O'Brien
2 hours ago

I am slightly dubious regarding returning true instead of 1. That doesn't seem to match anything described at codegolf.meta.stackexchange.com/questions/9263/…
– Sparr
1 hour ago

2

@Sparr Here is the current consensus.
– Arnauld
1 hour ago

Thanks. I put a new Answer on my link referring to that.
– Sparr
46 mins ago

add a comment |

up vote
2
down vote

JavaScript (Node.js), 51 46 43 bytes

Takes input as a BigInt literal. Returns true instead of 1.

f=(n,k=n)=>new Set(n+'').size>9||1+f(n*k,k)

Try it online!

edited 1 hour ago

answered 2 hours ago

Arnauld

71.9k688301

1

I keep forgetting JS has bigint's now :D
– Conor O'Brien
2 hours ago

I am slightly dubious regarding returning true instead of 1. That doesn't seem to match anything described at codegolf.meta.stackexchange.com/questions/9263/…
– Sparr
1 hour ago

2

@Sparr Here is the current consensus.
– Arnauld
1 hour ago

Thanks. I put a new Answer on my link referring to that.
– Sparr
46 mins ago

add a comment |

up vote
2
down vote

JavaScript (Node.js), 51 46 43 bytes

Takes input as a BigInt literal. Returns true instead of 1.

f=(n,k=n)=>new Set(n+'').size>9||1+f(n*k,k)

Try it online!

edited 1 hour ago

answered 2 hours ago

Arnauld

71.9k688301

JavaScript (Node.js), 51 46 43 bytes

Takes input as a BigInt literal. Returns true instead of 1.

f=(n,k=n)=>new Set(n+'').size>9||1+f(n*k,k)

Try it online!

edited 1 hour ago

answered 2 hours ago

Arnauld

71.9k688301

edited 1 hour ago

answered 2 hours ago

Arnauld

71.9k688301

answered 2 hours ago

Arnauld

71.9k688301

answered 2 hours ago

Arnauld

71.9k688301

1

I keep forgetting JS has bigint's now :D
– Conor O'Brien
2 hours ago

I am slightly dubious regarding returning true instead of 1. That doesn't seem to match anything described at codegolf.meta.stackexchange.com/questions/9263/…
– Sparr
1 hour ago

2

@Sparr Here is the current consensus.
– Arnauld
1 hour ago

Thanks. I put a new Answer on my link referring to that.
– Sparr
46 mins ago

add a comment |

1

I keep forgetting JS has bigint's now :D
– Conor O'Brien
2 hours ago

I am slightly dubious regarding returning true instead of 1. That doesn't seem to match anything described at codegolf.meta.stackexchange.com/questions/9263/…
– Sparr
1 hour ago

2

@Sparr Here is the current consensus.
– Arnauld
1 hour ago

Thanks. I put a new Answer on my link referring to that.
– Sparr
46 mins ago

I keep forgetting JS has bigint's now :D
– Conor O'Brien
2 hours ago

I am slightly dubious regarding returning true instead of 1. That doesn't seem to match anything described at codegolf.meta.stackexchange.com/questions/9263/…
– Sparr
1 hour ago

@Sparr Here is the current consensus.
– Arnauld
1 hour ago

Thanks. I put a new Answer on my link referring to that.
– Sparr
46 mins ago

add a comment |

up vote
0
down vote

J, 25 bytes

>:@]^:(10>#@~.@":@^)^:_&1

Try it online!

Single monadic verb. The input should be an extended-precision integer (e.g. 2x).

How it works

>:@]^:(10>#@~.@":@^)^:_&1    Monadic verb. Input: base a

    ^:              ^:_      Good old do-while loop.

                       &1    Given 1 as the starting point for b,

>:@]                         increment it each step

      (            )         and continue while the condition is true:

               ":@^          Digits of a^b

            ~.@              Unique digits

          #@                 Count of unique digits

       10>                   is less than 10

answered 2 hours ago

Bubbler

6,204759

add a comment |

up vote
0
down vote

J, 25 bytes

>:@]^:(10>#@~.@":@^)^:_&1

Try it online!

Single monadic verb. The input should be an extended-precision integer (e.g. 2x).

How it works

>:@]^:(10>#@~.@":@^)^:_&1    Monadic verb. Input: base a

    ^:              ^:_      Good old do-while loop.

                       &1    Given 1 as the starting point for b,

>:@]                         increment it each step

      (            )         and continue while the condition is true:

               ":@^          Digits of a^b

            ~.@              Unique digits

          #@                 Count of unique digits

       10>                   is less than 10

answered 2 hours ago

Bubbler

6,204759

add a comment |

up vote
0
down vote

J, 25 bytes

>:@]^:(10>#@~.@":@^)^:_&1

Try it online!

Single monadic verb. The input should be an extended-precision integer (e.g. 2x).

How it works

>:@]^:(10>#@~.@":@^)^:_&1    Monadic verb. Input: base a

    ^:              ^:_      Good old do-while loop.

                       &1    Given 1 as the starting point for b,

>:@]                         increment it each step

      (            )         and continue while the condition is true:

               ":@^          Digits of a^b

            ~.@              Unique digits

          #@                 Count of unique digits

       10>                   is less than 10

answered 2 hours ago

Bubbler

6,204759

J, 25 bytes

>:@]^:(10>#@~.@":@^)^:_&1

Try it online!

Single monadic verb. The input should be an extended-precision integer (e.g. 2x).

How it works

>:@]^:(10>#@~.@":@^)^:_&1    Monadic verb. Input: base a

    ^:              ^:_      Good old do-while loop.

                       &1    Given 1 as the starting point for b,

>:@]                         increment it each step

      (            )         and continue while the condition is true:

               ":@^          Digits of a^b

            ~.@              Unique digits

          #@                 Count of unique digits

       10>                   is less than 10

answered 2 hours ago

Bubbler

6,204759

answered 2 hours ago

Bubbler

6,204759

answered 2 hours ago

Bubbler

6,204759

answered 2 hours ago

Bubbler

6,204759

add a comment |

up vote
0
down vote

Jelly, 12 11 bytes

1*@ṾØDfƑʋ1#

Try it online!

How it works

1*@ṾØDfƑʋ1#  Main link. Argument: n



1            Set the return value to 1.

         1#  Call the link to the left for k = 1, 2, ... and with right argument n,

             until it returns a truthy value.

        ʋ      Combine the four links to the left into a dyadic chain.

 *@              Compute n**k.

   Ṿ             Convert it to its string representation.

    ØD           Yield "0123456789".

      fƑ         Filter and return 1 is the result is equal to the left argument.

edited 1 hour ago

answered 1 hour ago

Dennis♦

186k32295735

add a comment |

up vote
0
down vote

Jelly, 12 11 bytes

1*@ṾØDfƑʋ1#

Try it online!

How it works

1*@ṾØDfƑʋ1#  Main link. Argument: n



1            Set the return value to 1.

         1#  Call the link to the left for k = 1, 2, ... and with right argument n,

             until it returns a truthy value.

        ʋ      Combine the four links to the left into a dyadic chain.

 *@              Compute n**k.

   Ṿ             Convert it to its string representation.

    ØD           Yield "0123456789".

      fƑ         Filter and return 1 is the result is equal to the left argument.

edited 1 hour ago

answered 1 hour ago

Dennis♦

186k32295735

add a comment |

up vote
0
down vote

Jelly, 12 11 bytes

1*@ṾØDfƑʋ1#

Try it online!

How it works

1*@ṾØDfƑʋ1#  Main link. Argument: n



1            Set the return value to 1.

         1#  Call the link to the left for k = 1, 2, ... and with right argument n,

             until it returns a truthy value.

        ʋ      Combine the four links to the left into a dyadic chain.

 *@              Compute n**k.

   Ṿ             Convert it to its string representation.

    ØD           Yield "0123456789".

      fƑ         Filter and return 1 is the result is equal to the left argument.

edited 1 hour ago

answered 1 hour ago

Dennis♦

186k32295735

Jelly, 12 11 bytes

1*@ṾØDfƑʋ1#

Try it online!

How it works

1*@ṾØDfƑʋ1#  Main link. Argument: n



1            Set the return value to 1.

         1#  Call the link to the left for k = 1, 2, ... and with right argument n,

             until it returns a truthy value.

        ʋ      Combine the four links to the left into a dyadic chain.

 *@              Compute n**k.

   Ṿ             Convert it to its string representation.

    ØD           Yield "0123456789".

      fƑ         Filter and return 1 is the result is equal to the left argument.

edited 1 hour ago

answered 1 hour ago

Dennis♦

186k32295735

edited 1 hour ago

answered 1 hour ago

Dennis♦

186k32295735

answered 1 hour ago

Dennis♦

186k32295735

answered 1 hour ago

Dennis♦

186k32295735

add a comment |

up vote
0
down vote

Perl 6, 32 bytes

{first ($_** *).comb.Set>9,1..*}

Try it online!

Pretty self-explanatory.

Explanation

{                              }  # Anonymous code block

first                     ,1..*   # First positive number that

      ($_** *)    # When the input is raised to that power

              .comb.Set    # The set of digits

                       >9  # Is longer than 9

edited 56 mins ago

answered 2 hours ago

Jo King

20.5k246108

add a comment |

up vote
0
down vote

Perl 6, 32 bytes

{first ($_** *).comb.Set>9,1..*}

Try it online!

Pretty self-explanatory.

Explanation

{                              }  # Anonymous code block

first                     ,1..*   # First positive number that

      ($_** *)    # When the input is raised to that power

              .comb.Set    # The set of digits

                       >9  # Is longer than 9

edited 56 mins ago

answered 2 hours ago

Jo King

20.5k246108

add a comment |

up vote
0
down vote

Perl 6, 32 bytes

{first ($_** *).comb.Set>9,1..*}

Try it online!

Pretty self-explanatory.

Explanation

{                              }  # Anonymous code block

first                     ,1..*   # First positive number that

      ($_** *)    # When the input is raised to that power

              .comb.Set    # The set of digits

                       >9  # Is longer than 9

edited 56 mins ago

answered 2 hours ago

Jo King

20.5k246108

Perl 6, 32 bytes

{first ($_** *).comb.Set>9,1..*}

Try it online!

Pretty self-explanatory.

Explanation

{                              }  # Anonymous code block

first                     ,1..*   # First positive number that

      ($_** *)    # When the input is raised to that power

              .comb.Set    # The set of digits

                       >9  # Is longer than 9

edited 56 mins ago

answered 2 hours ago

Jo King

20.5k246108

edited 56 mins ago

answered 2 hours ago

Jo King

20.5k246108

answered 2 hours ago

Jo King

20.5k246108

answered 2 hours ago

Jo King

20.5k246108

add a comment |

up vote
0
down vote

Python 2, 44 bytes

f=lambda n,k=1:11>len(set(`k`))and-~f(n,n*k)

Input has to be a long, as `k` behaves differently for longs and ints.

Try it online!

answered 38 mins ago

Dennis♦

186k32295735

add a comment |

up vote
0
down vote

Python 2, 44 bytes

f=lambda n,k=1:11>len(set(`k`))and-~f(n,n*k)

Input has to be a long, as `k` behaves differently for longs and ints.

Try it online!

answered 38 mins ago

Dennis♦

186k32295735

add a comment |

up vote
0
down vote

Python 2, 44 bytes

f=lambda n,k=1:11>len(set(`k`))and-~f(n,n*k)

Input has to be a long, as `k` behaves differently for longs and ints.

Try it online!

answered 38 mins ago

Dennis♦

186k32295735

Python 2, 44 bytes

f=lambda n,k=1:11>len(set(`k`))and-~f(n,n*k)

Input has to be a long, as `k` behaves differently for longs and ints.

Try it online!

answered 38 mins ago

Dennis♦

186k32295735

answered 38 mins ago

Dennis♦

186k32295735

answered 38 mins ago

Dennis♦

186k32295735

answered 38 mins ago

Dennis♦

186k32295735

add a comment |

If this is an answer to a challenge…

…Be sure to follow the challenge specification. However, please refrain from exploiting obvious loopholes. Answers abusing any of the standard loopholes are considered invalid. If you think a specification is unclear or underspecified, comment on the question instead.

…Try to optimize your score. For instance, answers to code-golf challenges should attempt to be as short as possible. You can always include a readable version of the code in addition to the competitive one.
Explanations of your answer make it more interesting to read and are very much encouraged.

…Include a short header which indicates the language(s) of your code and its score, as defined by the challenge.

More generally…

…Please make sure to answer the question and provide sufficient detail.

…Avoid asking for help, clarification or responding to other answers (use comments instead).

draft saved

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This page is only for reference, If you need detailed information, please check here

Smallest Diversifying Exponent

Test cases

Test cases

Test cases

Test cases

5 Answers 5

JavaScript (Node.js), 51 46 43 bytes

J, 25 bytes

How it works

Jelly, 12 11 bytes

How it works

Perl 6, 32 bytes

Explanation

Python 2, 44 bytes

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5 Answers 5

5 Answers 5

JavaScript (Node.js), 51 46 43 bytes

JavaScript (Node.js), 51 46 43 bytes

JavaScript (Node.js), 51 46 43 bytes

JavaScript (Node.js), 51 46 43 bytes

J, 25 bytes

How it works

J, 25 bytes

How it works

J, 25 bytes

How it works

J, 25 bytes

How it works

Jelly, 12 11 bytes

How it works

Jelly, 12 11 bytes

How it works

Jelly, 12 11 bytes

How it works

Jelly, 12 11 bytes

How it works

Perl 6, 32 bytes

Explanation

Perl 6, 32 bytes

Explanation

Perl 6, 32 bytes

Explanation

Perl 6, 32 bytes

Explanation

Python 2, 44 bytes

Python 2, 44 bytes

Python 2, 44 bytes

Python 2, 44 bytes

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