The Squaring Sequence

Question

Each term in the squaring sequence, \$x_n\$, is created by taking \$x_{n-1}\$, squaring it, and removing all but the first four digits.

The sequence always begins with \$x_1 = 1111\$. Squaring this yields \$1234321\$, so \$x_2 = 1234\$

The first few terms are:

1111
1234
1522
2316
5363
...

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The Challenge

Your task is to, given a non-negative integer \$n\$, calculate \$x_n\$. You may submit a full program which performs I/O, or a function which takes \$n\$ as a parameter.

Your solution can be zero or one indexed, as long as you specify which.

Because all the terms in this sequence are shorter than 5 digits, your code should be as short as possible too. Standard code-golf loopholes apply.

May the best golfer win!

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Test Cases

Note: These are 1-indexed.

1   -> 1111
8   -> 6840
15  -> 7584
20  -> 1425
80  -> 4717

Answer 1

J-uby, 28 bytes

0-indexed.

(~:**&2|S|~:[]&4&0|Z)+[1111]

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Explanation

(~:** & 2 | S | ~:[] & 4 & 0 | Z) + [1111]

(                               ) + [1111]  # Iterate n times starting with initial value 1111
 ~:** & 2 |                                 #   Square, then
            S |                             #   Convert to string, then
                ~:[] & 4 & 0 |              #   Get first 4 characters, then
                               Z            #   Convert to int

Answer 2

q, 26 bytes

{"J"$4#string x*x}/[;1111]

k, 18 bytes

{.:4#$x*x}/[;1111]

Answer 3

Python 3, 76 bytes

x=1111
n=int(input())
for y in range(n-1):
    x=int(str(x**2)[:4])
print(x)

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Answer 4

><>, 40 36 bytes

"e"b*>$1-:@?!n:*v
%1:,av?  (*"dd":<-

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Explanation

                   # we call the input n
"e"b*              # initialize number as 1111
     >$1-:@?!n     # calculate n-1, if 0 then print number
              :*v  # else, square and move to row 2
     v?  (*"dd":<- # if number is less than 10000, move to row 2
%1:,a              # else divide by 10 and mod away the decimals to get an int