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Smallest number such that concatenation is a square

Challenge

Write a program or function that takes a number \$n\$ and returns the smallest \$k\$ such that concatenation \$n'k\$ is a square. This sequence is described by A071176 on the OEIS.

I/O Examples

input --> output

1   -->    6 (4^2)
10  -->    0 (10^2)
35  -->  344 (188^2)
164 -->  836 (406^2)
284 --> 2596 (1686^2)

Rules

Input will always be a positive decimal integer
Output will be a positive decimal integer with no leading 0's or 0
Standard I/O rules apply
No standard loopholes
This is code-golf, so shortest code in bytes wins

Answer*

# [05AB1E](https://github.com/Adriandmen/05AB1E/wiki/Commands), 7 [bytes](https://github.com/Adriandmen/05AB1E/wiki/Codepage)

∞<.Δ«Å²

[Try it online](https://tio.run/##yy9OTMpM/f//Ucc8G71zUw6tPtx6aNP//0YWJgA) or [verify all test cases](https://tio.run/##ATsAxP9vc2FiaWX/dnk/IiDihpIgIj95wqn/4oiePC7OlMKuc8Krw4XCsv99LP9bMSwxMCwzNSwxNjQsMjg0XQ).

# [05AB1E (legacy)](https://github.com/Adriandmen/05AB1E/tree/fb4a2ce2bce6660e1a680a74dd61b72c945e6c3b), 8 [bytes](https://github.com/Adriandmen/05AB1E/wiki/Codepage)

[N«Å²#}N

[Try it online](https://tio.run/##MzBNTDJM/f8/2u/Q6sOthzYp1/r9/29kYQIA) or [verify all test cases](https://tio.run/##ATcAyP8wNWFiMWX/dnk/IiDihpIgIj95wqn/W8KuTsKrw4XCsiN9Tv8s/1sxLDEwLDM1LDE2NCwyODRd).

Alternative 8-byter which works in both 05AB1E versions (credit to *@Grimmy*):

[N«Å²iNq

[Try it online](https://tio.run/##yy9OTMpM/f8/2u/Q6sOthzZl@hX@/29kYQIA) (no test suite due to the program terminate `q`).

**Explanation:**

∞         # Push an infinite list in the range [1, ...]
     <        # Decrease each by 1 to make the range [0, ...]
      .Δ      # Find the first value which is truthy for:
        «     #  Concat the value to the (implicit) input-integer
         Å²   #  And check whether it is a square number
              # (after which this found first value is output implicitly as result)

[         # Start an infinite loop:
     N«       #  Concat the 0-based loop index to the (implicit) input-integer
       Å²     #  If it's a square number:
         #    #   Stop the infinite loop
    }N        # After the infinite loop has stopped: push the last index
              # (after which this found index is output implicitly as result)

[         # Start an infinite loop:
     N«       #  Concat the 0-based loop index to the (implicit) input-integer
       Å²i    #  If it's a square number:
          N   #   Push the index again
           q  #   And terminate the program
              #   (after which this index is output implicitly as result)

The legacy version didn't had the `∞` builtin, and in the new version it isn't possible to push the last index `N` after a loop is terminated, which is why I decided to post both solutions.

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).

Edit Summary*

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\$\begingroup\$ Modern 6 with Δ«Å²Nα. \$\endgroup\$
– Grimmy
Commented Jan 17, 2020 at 12:40
3

\$\begingroup\$ Actually my suggested 6 fails for 183673469387755102041 (yes this is the smallest counter-example I could find). \$\endgroup\$
– Grimmy
Commented Jan 17, 2020 at 12:48
\$\begingroup\$ @Grimmy I was actually trying to find a counter example where n concatted with n in the first iteration would be square, but my test program timed out. That's unfortunate, but still very original approach! \$\endgroup\$
– Kevin Cruijssen
Commented Jan 17, 2020 at 12:49
\$\begingroup\$ @Grimmy: I'm not sure what your program does precisely, but it seems to me 13223140496 might be a smaller counterexample, as I expect an answer of 9685186064? \$\endgroup\$
– A. Rex
Commented Jan 18, 2020 at 3:13
\$\begingroup\$ @A.Rex Indeed, any number that is a square when concatenated to itself will be a counter-example. Those are fairly rare. \$\endgroup\$
– Grimmy
Commented Jan 18, 2020 at 10:52

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