#Brain-Flak , (削除) 84 (削除ここまで) 76 bytes Thanks to Wheat Wizard for golfing 8 bytes

Try it online! ##Explanation The program pushes the values from 0 to n-1 to the stack replaces the top 0 and 1 with 1 and 0. Then it multiplies the top of the stack by n and adds the value below it until there is only one value remaining on the stack.

Essentially it finds the digits for the smallest number in base n that contains n different digits (for n > 1 it's always of the form 1023...(n-1)). It then calculates the number given the digits and the base. ###Annotated Code (({})<>) # Pushes a copy of n to the right stack and switches to right stack {(({}[()]))}{} # While the top of the stack != 0 copy the top of the stack-1 # and push it (<{}{}>) # Discard the top two values (0 and 1 for n > 1) and push 0 ((())) # Push 1 twice (second time so that the loop is works properly) {{} # Loop while stack height > 1 ( # Push... {<({}[()])><>({})<>}{} # The top value of the stack * n {} # Plus the value below the top of the stack ) # End push ([][()])}{} # End loop

Brain-Flak , (削除) 84 (削除ここまで) 76 bytes

Thanks to Wheat Wizard for golfing 8 bytes

Try it online!

Explanation

The program pushes the values from 0 to n-1 to the stack replaces the top 0 and 1 with 1 and 0. Then it multiplies the top of the stack by n and adds the value below it until there is only one value remaining on the stack.

Essentially it finds the digits for the smallest number in base n that contains n different digits (for n > 1 it's always of the form 1023...(n-1)). It then calculates the number given the digits and the base.

Annotated Code

(({})<>) # Pushes a copy of n to the right stack and switches to right stack
{(({}[()]))}{} # While the top of the stack != 0 copy the top of the stack-1
 # and push it
(<{}{}>) # Discard the top two values (0 and 1 for n > 1) and push 0
((())) # Push 1 twice (second time so that the loop is works properly)
{{} # Loop while stack height > 1
 ( # Push...
 {<({}[()])><>({})<>}{} # The top value of the stack * n
 {} # Plus the value below the top of the stack
 ) # End push
([][()])}{} # End loop

#Brain-Flak, 84 bytes (({})<>){(({}[()]))}{}{}{}(()(<()>))([][()]){{}({<({}[()])><>({})<>}{}{})([][()])}{} Try it online! ##Explanation The program pushes the values from 0 to n-1 to the stack replaces the top 0 and 1 with 1 and 0. Then it multiplies the top of the stack by n and adds the value below it until there is only one value remaining on the stack.

Essentially it finds the digits for the smallest number in base n that contains n different digits (for n > 1 it's always of the form 1023...(n-1)). It then calculates the number given the digits and the base. ###Annotated Code (({})<>) # Pushes a copy of n to the right stack and switches to right stack {(({}[()]))}{} # While the top of the stack != 0 copy the top of the stack-1 # and push it {}{} # Discard the top two values (0 and 1 for n > 1) (()(<()>)) # Put 1 and 0 on the stack (1 on top) ([][()]){{} # Loop while stack height > 1 ( # Push... {<({}[()])><>({})<>}{} # The top value of the stack * n {} # Plus the value below the top of the stack ) # End push ([][()])}{} # End loop

#Brain-Flak, (削除) 84 (削除ここまで) 76 bytes Thanks to Wheat Wizard for golfing 8 bytes

(({})<>){(({}[()]))}{}(<{}{}>)((())){{}({<({}[()])><>({})<>}{}{})([][()])}{}

Try it online! ##Explanation The program pushes the values from 0 to n-1 to the stack replaces the top 0 and 1 with 1 and 0. Then it multiplies the top of the stack by n and adds the value below it until there is only one value remaining on the stack.

Essentially it finds the digits for the smallest number in base n that contains n different digits (for n > 1 it's always of the form 1023...(n-1)). It then calculates the number given the digits and the base. ###Annotated Code (({})<>) # Pushes a copy of n to the right stack and switches to right stack {(({}[()]))}{} # While the top of the stack != 0 copy the top of the stack-1 # and push it (<{}{}>) # Discard the top two values (0 and 1 for n > 1) and push 0 ((())) # Push 1 twice (second time so that the loop is works properly) {{} # Loop while stack height > 1 ( # Push... {<({}[()])><>({})<>}{} # The top value of the stack * n {} # Plus the value below the top of the stack ) # End push ([][()])}{} # End loop