Is it a Cyclic number?

Question

A cyclic number is a number of "n" digits that when multiplied by 1, 2, 3,...n, results in the same digits but in a different order.

For example, the number 142,857 is a cyclic number since 142,857 x 2 = 285,714, 142,857 x 3 = 428,571, 142,857 x 4 = 571,428, and so on. Given an integer input, determine if it is a cyclic number by outputting a truthy value if it is, and a falsy value if not.

Also, to be clear, the input can contain leading 0's: e.g. 0344827586206896551724137931

This is because, if leading zeros are not permitted on numerals, then 142857 is the only cyclic number in decimal.

Since it is code-golf, shortest answer in bytes wins!

Answer 1

05AB1E, 9 6 bytes

Thanks to Emigna for saving 3 bytes!

ā*€{ïË

Explanation:

ā        # Push range(1, len(input) + 1)
 *       # Multiply by the input
  €{     # Sort each element
    ï    # Convert to int to remove leading zeros
     Ë   # Check if all elements are equal

Uses the 05AB1E encoding. Try it online!

Answer 2

Actually, 18 bytes

;;ru@≈*♂$♂S♂≈╔@S≈=

Try it online! (expects quoted input)

Explanation:

;;ru@≈*♂$♂S♂≈╔@S≈=
;;                  duplicate input twice
  ru                range(1, len(input)+1)
    @≈              convert input to an integer
      *             multiply input by each element in range
       ♂$♂S♂≈       convert each product to a string, sort the digits, and convert back to int
             ╔      uniquify: remove duplicate elements
              @S≈   sort input and convert to int
                 =  compare equality

Answer 3

Python, 86 bytes

lambda n:all(sorted(n)==sorted(str(int(n)*i).zfill(len(n)))for i in range(2,len(n)+1))

Try it online!

Input numbers as strings.

Answer 4

PHP, 64 Bytes

for(;$i++<9;)$r+=($c=count_chars)($argn)==$c($argn*$i);echo$r>1;

Online Version

Answer 5

Haskell, 36 33 32 45 bytes

c n=let l=length n in(10^l-1)`div`read n==l+1

Example usage:

*Main> c "142857"
True

I don't think this algorithm needs any explanation.

TOL

Thanks for suggestions: Generic Display Name, Laikoni.

Thanks for correction: Antony Hatchkins.

EDIT Nope, fails on "33".

Answer 6

dc, 24 25 bytes

[1]sa0?dZd10r^1-r1+/rx=ap

Prints "0" if the number is not cyclic, otherwise "1". Requires the number to be entered as a string.

Example usage:

$ echo "[052631578947368421]" | dc -e '[1]sa0?dZd10r^1-r1+/rx=ap'
1
$ echo "[052631578947368422]" | dc -e '[1]sa0?dZd10r^1-r1+/rx=ap'
0

TOL

Explanation: Same algorithm as my Haskell submission.

EDIT Nope, fails on "33".

Answer 7

Mathematica, 81 bytes

Length@Union@PadLeft[Sort/@IntegerDigits[ToExpression@#*Range@StringLength@#]]<2&

Try it online!

input string

Input

"010309278350515463917525773195876288659793814432989690721649484536082474226804123711340206185567"

Output

True