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!

---

Test Cases

Note: These are 1-indexed.

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

Answer 1

JavaScript (ES7), 44 43 36 bytes

f=n=>--n?(f(n)**2+f).slice(0,4):1111

This is a great example of abusing type coercion: ** converts both its arguments to numbers, and + converts both its arguments to strings unless they're both numbers. This means that f(n)**2+f first converts f(n) to a number and squares it, then concatenates the result with the string representation of f. We can then use .slice to retrieve the first 4 chars of the string.

Here are a few alternate approaches that don't use strings:

f=(n,x=1111)=>x<1e4?--n?f(n,x*x):x:f(n,x/10|0)
f=n=>--n?(x=f(n))*x/(x>3162?1e4:1e3)|0:1111

Test snippet

let f=n=>--n?(Math.pow(f(n),2)+f).slice(0,4):1111

<input id=I type="number" step="1" min="1" value="1"><button onclick="console.log(f(I.value))">Run</button>

Note: this uses Math.pow because ** isn't supported in all browsers.

Answer 2

05AB1E, 8 7 bytes

Code:

$Fn4×4£

Explanation:

$        # Push 1 and the input
 F       # Input times do...
  n      #   Square the number
   4×    #   Repeat that string 4 times
     4£  #   Take the first four characters
         # Output the last computed number

Uses the CP-1252 encoding. Try it online!

Answer 3

Python 2, 51 46 44 Bytes

I'd like to get rid of the clunky if if possible, but I think an exec could be shorter.. Turns out for the moment that exec is shorter. Wrong again! The recursive function returns. This is one-indexed.

f=lambda n:1111*(n<2)or int(`f(n-1)**2`[:4])

An aleternative 46-byte solution with exec:

s=1111;exec's=int(`s*s`[:4]);'*input();print s

An alternative 49-byte recursive solution:

f=lambda n,s=1111:s*0**n or f(n-1,int(`s*2`[:4]))

^{Thanks to Flp.Tkc for saving a byte by reminding me that squaring doesn't need exponentiation :)}

Answer 4

Haskell, 40 bytes

((iterate(read.take 4.show.(^2))1111)!!)

It's a 0-based sequence. Usage example: ((iterate(read.take 4.show.(^2))1111)!!) 79 -> 4717.

How it works:

iterate (   ) 1111               -- repeatedly apply a function starting
                                 -- with 1111 and collect the results in a list
                                 -- the function is
           (^2)                  -- square
        show                     -- turn into string
     take 4                      -- take the first 4 chars
  read                           -- turn back to number
                     !!          -- finally pick the nth element from the list         

Answer 5

Perl, 37 bytes

36 bytes of code + -p flag.

$\=1x4;$\=substr$\*$\,0,4while--$_}{

To run it:

perl -pe '$\=1x4;$\=substr$\*$\,0,4while--$_}{' <<< 80

Answer 6

V, 19 bytes

4é1Àñ|C="*"
5|D

Try it online!

This uses 0-based indexing.

Of course, since numbers aren't exactly V's forte, this isn't very golfy. However, it does show one nice advantage V has over vim. You can run a macro 0 times, which is not possible in vim since '0' is a command not a count.

This contains many unprintable characters, so here is a hexdump:

0000000: 34e9 31c0 f17c 4312 3d12 222a 1222 0a1b  4.1..|C.=."*."..
0000010: 357c 44                                  5|D

And here is a readable version:

4é1Àñ|C<C-r>=<C-r>"*<C-r>"
<esc>5|D

Explanation:

4                           " 4 times:
 é1                         " Insert a '1'
   Àñ                       " Arg1 times:
     |                      "   Move to the first character on this line
      C                     "   Delete this whole line and enter insert mode
       <C-r>=               "   Insert the following evaluated as vimscript:
             <C-r>"         "     Insert what we just deleted
                   *        "     Times
                    <C-r>"  "     What we just deleted
<esc>                       "   Escape to normal mode
     5|                     "   Move to the fifth column on this line
       D                    "   And delete until the end of this line
                            " The second 'ñ' is added implicitly

Answer 7

Mathematica, 48 bytes

Nest[⌊10^(3-⌊t=2Log[10,#]⌋+t)⌋&,1111,#]&

Unnamed function taking an integer argument; 0-indexed. Uses four three-byte characters ⌊⌊⌋⌋: Mathematica uses either Floor[x] or ⌊x⌋ to round a real number down to an integer, and the latter is generally one fewer byte. The command names in Mathematica for converting integers to strings are too long, so instead we do a mathematical calculation to find the first four digits of x^2: we take the base-10 logarithm of x^2, subtract its integer part, raise 10 back to that power, and multiply by 1000 and round down.

tl;dr: logarithms ftw

Answer 8

Jelly, 12 9 bytes

-3 bytes thanks to Dennis using 1-based indexing and the ṁ mold/reshape atom. Golfing suggestions welcome! Try it online!

²Dṁ4Ḍ
1Ç¡

Ungolfing

Helper link
²       Square.
 D      Integer to decimal (a list of digits).
  ṁ4    Mold/reshape list_of_digits to be 4 digits long.
    Ḍ   Decimal to integer.

Main link: implicit left argument n
1     Start with the nilad 1.
 Ç¡   Call the helper link n times.

Answer 9

APL (Dyalog Extended), 13 bytes

-2 (changing the input method) thanks to @Razetime

{⍎4⍴⍕⍵*2}⍣⎕⊢1

Explanation:

{⍎4⍴⍕⍵*2}⍣⎕⊢1     ⍝ apply the dfn input times
            1     ⍝ .. with initial argument 1
     ⍵*2          ⍝ current value squared
 ⍎4⍴⍕             ⍝ take first 4 digits

Try it online!

Answer 10

Powershell, 73 55 bytes

Huge thanks to TimmyD for shaving off 18 bytes!

Code:

for($A=1111;$args[0]---1;$A=-join"$(+$A*$A)"[0..3]){}$A

$A=1111;1..($n=2)|%{[string]$B=[math]::pow($A,2);$A=$B.substring(0,4)};$A

$n is n in x_n-1

Explanation and exploded code:

$A=1111                            #starting number
$n=4                               #n in formula
for($i=0; $i -lt $n;$i++)          #loop n times
{
    [string]$B=[math]::pow($A,2)   #create a new string $B and set it to $A raised to the power of 2
    $A=$B.substring(0,4)           #set $A to the first 4 characters of $B
}
$A                             #print $A

Some notes:

• Powershell lets you assign variables in the same statements where you reference them. For example, 1..($n=4)|% will set $n to 4 and then start a loop that runs $n times. 1 can be changed to any integer and it will loop $n-[your integer]+1 times.
• The default data type when using [math]:: in Powershell is a double. In the code above, we have to explicitly cast $B to a string so that we can call .substring() on it because there is no .substring() function for doubles in Powershell.

Answer 11

Python 2,  44  41 bytes

-3 bytes thanks to xnor (use an integer division to avoid and)

f=lambda n:int(1/n*1111or`f(n-1)**2`[:4])

repl.it

1-based recursive function.

When n>1 the integer division, 1/n, results in 0, then 0*1111=0 which is falsey, so the right of the or is evaluated, which takes the first four characters of the representation of the square of the n-1th result; this is then cast to an int.

When n=1 the integer division, 1/n, results in 1, then 1*1111=1111, which is truthy, and the int 1111 cast to an int is 1111.

Answer 12

Groovy, 49 bytes

{x=1111;(it-1).times{x="${x**2}"[0..3] as int};x}

Answer 13

Pyke, 10 bytes

1RVX`4*4<b

Try it here!

Answer 14

MATL, 14, 13 bytes

1111G:"UV4:)U

Try it online!

Explanation:

1111            % Push 1111
    G           % Push input
     :"         % Input times:
       U        %   Square the top of the stack
        V       %   Convert it to a string
         4:)    %   Take the first four digits
            U   %   Convert it back to a number
                % Implictly display

Answer 15

R, 58 56 55 53 bytes

x=3334;for(e in N<-scan():1)x=x^2%/%10^(3+(x>3162));x

Takes N from stdin. 3334 is practically X_0, which is needed because the for-loop needs to be executed at least once (it would be longer to skip).

R really is a terrible language for taking the first four digits of a number, but since the number of cases are limited, we only have to worry about the squares of x<3163 and x>3162, the former yield a 6 digit number, the latter a 7 digit number.

The rest is pretty straightforward, %/% divides and ignores the remainder. x is printed to stdout.

Saved 2 bytes thanks to @ETHproductions

Answer 16

Javagony - 153 bytes

Javagony is a restricted version of Java, that doesn't allow any control flow except recursion and try-catch, no for loops, while loops, or if's. Coding in it is a pretty fun exercise, but frustrating. Not that regular Java isn't nearly as frustrating by itself.

int a(int i){return a(i-1,1111);}int a(int i,int n){try{int x=1/i;return a(i-1,Integer.parseInt((n*n+"").substring(0,4)));}catch(Exception e){return n;}}

Answer 17

PHP, 55 52 bytes

Saved 3 bytes thanks to @user59178

for($i=1111;$argv[1]--;)$i=substr($i**2,0,4);echo$i;

Run from command line, zero-indexed.

Thanks for not caring about what type my variables are, PHP! Here we simply square the number and trim off everything past the first 4 digits, casually alternating between number and string without a care in the world.

Answer 18

cQuents, 14 bytes

=1111:(ZZ)[:4]

Try it online!

1-indexed.

Explanation

=1111           first term is 1111
     :          given n, output nth term, otherwise output full sequence
                each term equals
      (ZZ)                       previous term * previous term
          [:4]                                                 [:4] (python slicing)

Answer 19

Pushy, 20 bytes

1111@:2esL4-:.;Kjk;#

Try it online!

Note this is 1-indexed.

            % Implicit: N is on stack
1111@       % Push 1111, and then reverse stack to get [1111, n]
:           % N times do: (this consumes N)
 2e         %   Square last term
 s          %   Split into individual digits
 L4-:.;     %   Get stack length -4, pop that many times
 Kj         %   Join remaining digits (Uses flag "K" for whole stack)
 k          %   Set "K" flag to false, so operations only affect last item
;           % End loop.       
#           % Output final calculated term

Answer 20

Brachylog, 18 bytes

,1111:?:{^@[.l4,}i

Try it online!

This answer is 0-indexed.

Explanation

,1111:?:{       }i      Iteratively call Input times the predicate in brackets starting with
                          input 1111:

         ^                  Square
          @[.               Output is a prefix of the square
            .l4,            Its length is 4

Answer 21

Batch, 82 bytes

@set n=1111
@for /l %%i in (1,1,%1)do @set/an*=n&call set n=%%n:~0,4%%
@echo %n%

Like Perl, integers are strings, but unlike Perl I can only take the substring of a variable, and taking substrings inside a loop is somewhat awkward.

Answer 22

C, 56 bytes

a;s(n){for(a=1111;--n;)a=a*a/(a>3162?1e4:1e3);return a;}

One-indexed.

Answer 23

Clojure, 76 bytes

(defn s[n](if(= n 1)1111(read-string(subs(str(*(s(dec n))(s(dec n))))0 4))))

First Clojure golf (seems like a nice language). This is 1-indexed.

Will explain the code later.

Answer 24

C#, 64 60 bytes

Saved 4 bytes by following Olivier Grégoire's comment on a Java answer!

n=>{int x=1111;for(;n-->1;)for(x*=x;x>1e4;x/=10);return x;};

Previous version (64 bytes):

n=>{int x=1111;while(n-->1){x*=x;while(x>9999)x/=10;}return x;};

Full program with ungolfed method and test cases:

using System;

namespace SquaringSequence
{
    class Program
    {
        static void Main(string[] args)
        {
            Func<int, int> f = n =>
            {
                int x = 1111;
                while (n-- > 1)
                {
                    x *= x;
                    while (x > 9999)
                        x /= 10;
                }
                return x;
            };

            // test cases:
            Console.WriteLine(f(1));    // 1111
            Console.WriteLine(f(8));    // 6840
            Console.WriteLine(f(15));   // 7584
            Console.WriteLine(f(20));   // 1425
            Console.WriteLine(f(80));   // 4717
        }
    }
}

Answer 25

Ruby, 47 bytes

First golf! Saves bytes with -n option (but still count as 1! :)).

a=1111;$_.to_i.times{a="#{a*a}"[0,4].to_i};p a

0-indexed. To run it:

ruby -ne 'a=1111;$_.to_i.times{a="#{a*a}"[0,4].to_i};p a' <<< 80

Answer 26

Pyth, 13 12 bytes

Thanks to @Jakube for -1 byte

us<*4`*GG4Q1

A program that takes input of a 1-indexed integer and prints the result.

Test suite

This uses a similar approach to @Adnan's answer.

How it works

us<*4`*GG4Q1  Program. Input: Q
u         Q1  Execute the following Q times, starting at 1, with variable G:
      *GG      Yield G*G
     `          Convert to string
   *4           Repeat 4 times
  <      4      Yield first 4 characters
 s              Convert to integer
              Implicitly print

Answer 27

GolfScript, 15 bytes

~1111\{.*`4<~}*

Try it online!

0-indexed

~                 # Parse n to a number
 1111             # Push 1111
     \{      }*   # Execute this block n times
       .*         # Square the number
         `        # Parse it to a string
          4<      # Get the first 4 digits
            ~     # Parse it back to a number

Answer 28

Vyxal, 6 5 bytes

Ṫ(²4Ẏ

Try it online, or verify all test cases.

Explanation:

Ṫ      # Pop, push 1 then the input
 (     # [Input] times:
  ²    #   Square
   4Ẏ  #   Get the first 4 digits

Answer 29

TI-Basic, 31 bytes

Input N
1111
For(I,2,N
int(Ans²/₁₀^(-3+int(log(Ans²
End
Ans

1-indexed input. - represents the negative symbol.

Answer 30

Excel VBA, 42 bytes

v=1111:For i=2To[A1]:v=Left(v^2,4):Next:?v

Input is in cell A1 of the active sheet. Code is run in the immediate window. Output is to the immediate window. Here's the result for 80 as an input: