find the pattern in this number sequence of 1's and 0's

Question

Write the shortest program or function which generates these 1000 numbers or a sequence (0- or 1-indexed) which begins with them.

[0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 
 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 
 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 
 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 
 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 
 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 
 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 
 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 
 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 
 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 
 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 
 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 
 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 
 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 
 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 
 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 
 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 
 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 
 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 
 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 
 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 
 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 
 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 
 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 
 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 
 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 
 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 
 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 
 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 
 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 
 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 
 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 
 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 
 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 
 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 
 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 
 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 
 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 
 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 
 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 
 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 
 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0]

this is my first time posting a code puzzle. if you have any style improvements. let me know. — john mangual, Commented Apr 18, 2018 at 20:41
Hi John, and welcome to PPCG! Challenges here need to have an objective win condition (usually code-golf). We also recommend running all challenges through the sandbox before posting. — user48543, Commented Apr 18, 2018 at 20:47
As the goal of this problem seems to be finding the sequence, I'd recommend asking for the shortest code that will generate these first 1000 elements correctly. — user48543, Commented Apr 18, 2018 at 20:52
@Mnemonic that sounds about right. My code is already quite short, and I'm asking if there's an even shorter code. Feel free to edit :-) or I can just move to sandbox — john mangual, Commented Apr 18, 2018 at 20:56
I forget who did this challenge before. But it was very well received to "find the pattern". I vaguely remember someone cracking it in 50 minutes; but people continued to answer even after that. — Magic Octopus Urn, Commented Apr 23, 2018 at 0:22

ETHproductions · Accepted Answer · 2018-04-19 19:57:14Z

19

Jelly, 11 10 bytes

Saved 1 byte thanks to @Dennis

ȷḶ×⁽q£:ȷ5Ḃ

Try it online!

How?

I first noticed that the pattern alternates between runs of length 4 and length 3, skipping the length-4 step every few runs. This led me to look for a number which could be divided into the current index, then taken mod 2 and floored—i.e. retrieving the least significant bit—to give the bit at that index in the series. After much trial and error, I found that 3.41845 does exactly that, but multiplying by its approximate reciprocal (.29253) is a byte shorter.

ȷḶ×⁽q£:ȷ5Ḃ    Main link. Arguments: none
ȷ             Yield 1e3, i.e. 1000.
 Ḷ            Lowered range; yield [0, 1, 2, ..., 999].
  ×⁽q£        Multiply each item by 29253.
      :ȷ5     Floor-divide each item by 1e5, i.e. 100000.
         Ḃ    Take each item mod 2.

edited Apr 19, 2018 at 19:57

answered Apr 18, 2018 at 22:07

ETHproductions

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\$\begingroup\$ ah you found it \$\endgroup\$
– Jonathan Allan
Commented Apr 18, 2018 at 22:11
\$\begingroup\$ [0...999] times each by 0.2925, mod 2 and floor (I'd go floor then mod 2 but equivalent) \$\endgroup\$
– Jonathan Allan
Commented Apr 18, 2018 at 22:14
8

\$\begingroup\$ Well that's quite anticlimactic, was expecting something more intricate. \$\endgroup\$
– Etheryte
Commented Apr 18, 2018 at 22:16
\$\begingroup\$ @JonathanAllan I originally tried just Ḃ but apparently that's just mod 2 rather than lowest bit, so I added the Ḟ to fix it. Swapped now \$\endgroup\$
– ETHproductions
Commented Apr 18, 2018 at 22:21
1

\$\begingroup\$ ȷḶ×⁽q£:ȷ5Ḃ works, for 10 bytes. \$\endgroup\$
– Dennis
Commented Apr 19, 2018 at 2:45

| Show 3 more comments

G B · Accepted Answer · 2018-04-19 10:11:42Z

6

Ruby, 34 29 26 22 bytes

$.+=184while p$./629%2

Try it online!

Quick explanation: this works because of the magic number 629. I noticed that the sequence starts repeating after the 629th element, and I tried to "improve" some existing answer, using only integer math. I found that the other "magic number" (0.29253) is actually 184/629.

edited Apr 19, 2018 at 10:11

answered Apr 19, 2018 at 8:52

G B

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dzaima · Accepted Answer · 2018-04-18 21:51:53Z

3

Dyalog APL, 99 83 82 bytes

a←{⍵/0 1}¨(↓3 2⍴4 3 3)
{a⊢←↓⍉↑a{⍺∘{⍵/⊂⍺}¨⍵}¨↓3 3⍴⍵}¨(9/5)∘⊤¨1386531 496098
1000⍴∊a

Try it online!

Definitely not the intended solution as this still has a lot of hardcoded data, but it's a start.

edited Apr 18, 2018 at 21:51

answered Apr 18, 2018 at 21:45

dzaima

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Jonathan Allan · Accepted Answer · 2018-04-18 22:21:03Z

Jelly, 31 bytes

Given the pattern there is probably an even shorter way...

ĖŒṙḂ
“ṁ⁽⁺ḄæI’BḤ+3żḂ$ẎÇo2Ç+3Çḣȷ¬

Try it online!

How?

Exploits the repeating run length structure that is apparent to a depth of three.

ĖŒṙḂ - Link 1, make runs of bits: list of lengths    e.g. [5,3,5,3,3]
Ė    - enumerate                      [[1,5],[2,3],[3,5],[4,3],[5,3]]
 Œṙ  - run-length decode      [1,1,1,1,1,2,2,2,3,3,3,3,3,4,4,4,5,5,5]
   Ḃ - bit (modulo by 2)      [1,1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,1,1,1]

“ṁ⁽⁺ḄæI’BḤ+3żḂ$ẎÇo2Ç+3Çḣȷ¬ - Main link: no arguments
“ṁ⁽⁺ḄæI’                   - literal 234931870193324
        B                  - to binary = [1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,1,0,0]
         Ḥ                 - double    = [2,2,0,2,0,2,0,2,2,0,2,0,2,0,2,2,0,2,0,2,0,2,2,0,2,0,2,0,2,0,2,2,0,2,0,2,0,2,2,0,2,0,2,0,2,2,0,0]
          +3               - add three = [5,5,3,5,3,5,3,5,5,3,5,3,5,3,5,5,3,5,3,5,3,5,5,3,5,3,5,3,5,3,5,5,3,5,3,5,3,5,5,3,5,3,5,3,5,5,3,3]
              $            - last two links as a monad:
             Ḃ             -   bit     = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
            ż              -   zip     = [[5,1],[5,1],[3,1],[5,1],[3,1],[5,1],[3,1],[5,1],[5,1],[3,1],[5,1],[3,1],[5,1],[3,1],[5,1],[5,1],[3,1],[5,1],[3,1],[5,1],[3,1],[5,1],[5,1],[3,1],[5,1],[3,1],[5,1],[3,1],[5,1],[3,1],[5,1],[5,1],[3,1],[5,1],[3,1],[5,1],[3,1],[5,1],[5,1],[3,1],[5,1],[3,1],[5,1],[3,1],[5,1],[5,1],[3,1],[3,1]]
               Ẏ           - tighten   = [5,1,5,1,3,1,5,1,3,1,5,1,3,1,5,1,5,1,3,1,5,1,3,1,5,1,3,1,5,1,5,1,3,1,5,1,3,1,5,1,3,1,5,1,5,1,3,1,5,1,3,1,5,1,3,1,5,1,3,1,5,1,5,1,3,1,5,1,3,1,5,1,3,1,5,1,5,1,3,1,5,1,3,1,5,1,3,1,5,1,5,1,3,1,3,1]
                Ç          - call the last Link (1) as a monad
                           -           = [1,1,1,1,1,0,1,1,1,1,1,0,1,1,1,0,1,1,1,1,1,0,1,1,1,0,1,1,1,1,1,0,1,1,1,0,1,1,1,1,1,0,1,1,1,1,1,0,1,1,1,0,1,1,1,1,1,0,1,1,1,0,1,1,1,1,1,0,1,1,1,0,1,1,1,1,1,0,1,1,1,1,1,0,1,1,1,0,1,1,1,1,1,0,1,1,1,0,1,1,1,1,1,0,1,1,1,0,1,1,1,1,1,0,1,1,1,1,1,0,1,1,1,0,1,1,1,1,1,0,1,1,1,0,1,1,1,1,1,0,1,1,1,0,1,1,1,1,1,0,1,1,1,0,1,1,1,1,1,0,1,1,1,1,1,0,1,1,1,0,1,1,1,1,1,0,1,1,1,0,1,1,1,1,1,0,1,1,1,0,1,1,1,1,1,0,1,1,1,1,1,0,1,1,1,0,1,1,1,1,1,0,1,1,1,0,1,1,1,1,1,0,1,1,1,0,1,1,1,1,1,0,1,1,1,1,1,0,1,1,1,0,1,1,1,0]
                 o2        - OR 2      = [1,1,1,1,1,2,1,1,1,1,1,2,1,1,1,2,1,1,1,1,1,2,1,1,1,2,1,1,1,1,1,2,1,1,1,2,1,1,1,1,1,2,1,1,1,1,1,2,1,1,1,2,1,1,1,1,1,2,1,1,1,2,1,1,1,1,1,2,1,1,1,2,1,1,1,1,1,2,1,1,1,1,1,2,1,1,1,2,1,1,1,1,1,2,1,1,1,2,1,1,1,1,1,2,1,1,1,2,1,1,1,1,1,2,1,1,1,1,1,2,1,1,1,2,1,1,1,1,1,2,1,1,1,2,1,1,1,1,1,2,1,1,1,2,1,1,1,1,1,2,1,1,1,2,1,1,1,1,1,2,1,1,1,1,1,2,1,1,1,2,1,1,1,1,1,2,1,1,1,2,1,1,1,1,1,2,1,1,1,2,1,1,1,1,1,2,1,1,1,1,1,2,1,1,1,2,1,1,1,1,1,2,1,1,1,2,1,1,1,1,1,2,1,1,1,2,1,1,1,1,1,2,1,1,1,1,1,2,1,1,1,2,1,1,1,2]
                   Ç       - Link 1... = [1,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0,1,0,0,1,0,1,0,0]
                    +3     - add three = [4,3,4,3,4,3,3,4,3,4,3,4,3,3,4,3,4,3,3,4,3,4,3,4,3,3,4,3,4,3,3,4,3,4,3,4,3,3,4,3,4,3,3,4,3,4,3,4,3,3,4,3,4,3,4,3,3,4,3,4,3,3,4,3,4,3,4,3,3,4,3,4,3,3,4,3,4,3,4,3,3,4,3,4,3,3,4,3,4,3,4,3,3,4,3,4,3,4,3,3,4,3,4,3,3,4,3,4,3,4,3,3,4,3,4,3,3,4,3,4,3,4,3,3,4,3,4,3,3,4,3,4,3,4,3,3,4,3,4,3,4,3,3,4,3,4,3,3,4,3,4,3,4,3,3,4,3,4,3,3,4,3,4,3,4,3,3,4,3,4,3,3,4,3,4,3,4,3,3,4,3,4,3,3,4,3,4,3,4,3,3,4,3,4,3,4,3,3,4,3,4,3,3,4,3,4,3,4,3,3,4,3,4,3,3,4,3,4,3,4,3,3,4,3,4,3,3,4,3,4,3,4,3,3,4,3,4,3,4,3,3,4,3,4,3,3,4,3,4,3,4,3,3,4,3,4,3,3,4,3,4,3,4,3,3,4,3,4,3,3,4,3,4,3,4,3,3,4,3,4,3,4,3,3,4,3,4,3,3,4,3,4,3,3]
                      Ç    - Link 1... = [1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0]
                        ȷ  - literal 1000
                       ḣ   - head      = [1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1]
                         ¬ - NOT       = [0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0]

Welcome to PPCG :) - it's a golfing language written by one of our moderators, Dennis. Click in the header for it's git-hub page where there is a wiki. — Jonathan Allan, Commented Apr 18, 2018 at 22:03
i promise to get better at posing questions. i see there's a sandbox and some standard formatting. — john mangual, Commented Apr 18, 2018 at 22:05
@EsolangingFruit I thought as I was doing it that it could be a fraction doing the repetition... 117/400 it seems! — Jonathan Allan, Commented Apr 18, 2018 at 22:22

Community · Accepted Answer · 2020-06-17 09:04:33Z

Java 8, 75 64 62 bytes

v->{for(int i=0;i<1e3;)System.out.print((int)(i++*.29253)%2);}

Prints the entire sequence without delimiter to save bytes, because they will only be 0 and 1 anyway.

Ports of @ETHproductions' Jelly answer, because I doubt I find anything shorter..

Try it online.

Explanation:

v->{                     // Method with empty unused parameter and no return-type
  for(int i=0;i<1e3;)    //  Loop `i` in range [0,1000)
    System.out.print(    //   Print:
      (int)(i++*.29253)  //    `i` multiplied with 0.29253,
                         //    and then truncated of their decimal values by casting to int
      %2);}              //    Modulo-2 to result in either 0 or 1

Old answer returning the resulting array (75 bytes):

v->{int i=1000,r[]=new int[i];for(;i-->0;)r[i]=(int)(i*.29253)%2;return r;}

Try it online.

Explanation:

v->{                   // Method with empty unused parameter and integer-array return-type
  int i=1000,          //  Index `i`, starting at 1000
      r[]=new int[i];  //  Result-array of size 1000
  for(;i-->0;)         //  Loop `i` in range (1000,0]
    r[i]=              //   Set the item in the array at index `i` to:
      (int)(i*.29253)  //    `i` multiplied with 0.29253,
                       //    and then truncated of their decimal values by casting to int
      %2;              //    Modulo-2 to result in either 0 or 1
  return r;}           //  Return the resulting integer-array

Kelly Lowder · Accepted Answer · 2018-04-20 04:37:57Z

Wolfram Language (Mathematica), 96 bytes

I searched for a cellular automaton that looks at the 4 neighbors to the left and produces the walking left pattern seen in the data when you Partition the data into length 7 and keep every third row.

This cellular automaton will run for 29 generations each of which is triplicated, matching the sequence perfectly for characters 1 to 629. However the sequence starts repeating at the 630th character rather than continuing the observed pattern, so extra code is needed to handle the repeat of the truncated pattern. I generate the main pattern twice to get to 1258 characters.

Most@Flatten[{#,#,#}&/@CellularAutomaton[{271,2,-{{4},{3},{2},{1}}},{0,0,0,0,1,1,1},29]]~Table~2

Without that glitch we could do it in a shorter 74 bytes. The 47 is the number of generations needed to get to 1000 characters (this actually goes to 1008=48*7*3)

{#,#,#}&/@CellularAutomaton[{271,2,-{{4},{3},{2},{1}}},{0,0,0,0,1,1,1},47]

Try it online!

DialFrost · Accepted Answer · 2023-01-02 09:55:35Z

3

Python 3, 42 bytes

x=184
while x/629%2:print(x//629%2);x+=184

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Port of G.B.'s answer.

answered Jan 2, 2023 at 9:55

DialFrost

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l4m2 · Accepted Answer · 2018-04-19 18:33:36Z

2

JavaScript (Node.js), 41 33 bytes, port

Thank Rick Hitchcock for 4+ bytes

f=i=>i>999?'':(i*.29253&1)+f(-~i)

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JavaScript (Node.js), 121 bytes, original

_=>'8888y888'[s='replace'](/8/g,'aaa3yyy')[s](/y/g,'aaa3aa3')[s](/a/g,34)[s](/./g,t=>(_=+!+_+[]).repeat(t)).slice(3,1003)

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edited Apr 19, 2018 at 18:33

answered Apr 19, 2018 at 10:11

l4m2

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\$\begingroup\$ Save 4 bytes using recursion: f=(i=0)=>i<1e3?(i*.29253&1)+f(i+1):'' \$\endgroup\$
– Rick Hitchcock
Commented Apr 19, 2018 at 17:58

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Khuldraeseth na'Barya · Accepted Answer · 2018-04-19 20:26:13Z

2

Stax, 13 11 bytes

í?♫~╘äqx-G▄

Run and debug it at staxlang.xyz!

Port to Stax of @ETHproductions's Jelly answer (before its modification) with some modifications by @recursive to save two bytes.

edited Apr 19, 2018 at 20:26

answered Apr 18, 2018 at 22:51

Khuldraeseth na'Barya

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\$\begingroup\$ You can double the denominator, keep the fractional part, and then round to nearest integer rather than using modulus. If I'm not mistaken, this also gives 11 \$\endgroup\$
– recursive
Commented Apr 18, 2018 at 23:54

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lynn · Accepted Answer · 2018-06-18 14:43:35Z

Z80Golf, 27 bytes

00000000: 018d 2b7b 1f1f e601 f630 ff09 3001 1313  ..+{.....0..0...
00000010: 7bfe 9220 ee7a fe04 20e9 76              {.. .z.. .v

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Translated from this C code:

for (n = 0; n >> 16 != 1170; n += 11149 + 65536)
    putchar('0'|n>>18&1);

Disassembly:

  ld bc, 11149
loop:
  ld a, e
  rra
  rra
  and 1
  or '0'
  rst $38           ; putchar
  add hl, bc        ; Add 11149 to n = DEHL.
  jr nc, just_one   ; Add 65536 to n, possibly with carry from low 16 bits.
  inc de
just_one:
  inc de
  ld a, e
  cp 1170 & 255
  jr nz, loop
  ld a, d
  cp 1170 >> 8
  jr nz, loop
  halt

This is essentially a fixed-point arithmetic approach: (11149 + 65536) / 2¹⁸ ≈ 0.29253, the constant used by other answers.

Galen Ivanov · Accepted Answer · 2018-04-19 07:03:14Z

1

J, 17 bytes

2|<.0.29253*i.1e3

A J port of ETHproduction's Jelly answer.

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answered Apr 19, 2018 at 7:03

Galen Ivanov

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Shaggy · Accepted Answer · 2018-04-19 08:22:13Z

1

Japt, 13 bytes

A³Ç*.29#ý f u
A³             // Given 10³,
  Ç            // map over it as a range, returning the given number
   *.29253     // times the constant,
           f u // floored and mod-2.

Japt version of ETHproduction's Jelly answer.
Bug fixed thanks to Oliver.

Try it here.

edited Apr 19, 2018 at 8:22

Shaggy

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answered Apr 18, 2018 at 23:47

Etheryte

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Neil · Accepted Answer · 2018-04-19 11:04:24Z

Charcoal, 13 bytes

Ｅφ§01×·²⁹²⁵³ι

Try it online! Link is to verbose version of code. Explanation:

 φ              Predefined variable 1000
Ｅ               Map over implicit range
            ι   Current value
      ·²⁹²⁵³    Literal constant `0.29253`
     ×          Multiply
   01           Literal string `01`
  §             Cyclically index
                Implicitly print each result on its own line

Thanks to @ASCII-only for allowing indexing to accept floats which are cast to integer (and then automatically reduced modulo 2 in this case).

Community · Accepted Answer · 2020-06-17 09:04:33Z

1

C, 55 53 52 bytes

f(i,j){for(i=0;j=.29253*i,i++-1e3;)putchar(j%2+48);}

Port of Kevin Cruijssen's Java answer. Try it online here.

Thanks to vazt for golfing 2 bytes and to Jonathan Frech for golfing one more.

Ungolfed version:

f(i, j) { // function taking two dummy arguments (implicitly int) and implicitly returning an unused int
    for(i = 0; j = .29253*i, i++ - 1e3; ) //  loop 1000 times, multiply i with 0.29253, truncating to an integer
        putchar(j % 2 + 48);  // modulo the truncated integer by 2, yielding 0 or 1, then convert to ASCII (48 is ASCII code for '0') and print
}

edited Jun 17, 2020 at 9:04

CommunityBot

1

answered Apr 19, 2018 at 9:51

O.O.Balance

1,6091 gold badge9 silver badges19 bronze badges

\$\begingroup\$ i is initialized to 0 since it's global, so you can remove the i=0 from the for-loop initializer to save 3 bytes. Also if you introduce a second variable (as a parameter to f()) and assign i++*.29253 to it, you can avoid the cast and save another 2 bytes: i;f(j){for(;i<1e3;)printf("%d",(j=i++*.29253)%2);} Try it online! \$\endgroup\$
– vazt
Commented Apr 19, 2018 at 14:03
\$\begingroup\$ @vazt Yes, i is initialized to 0 in the beginning, but if we want to call this function more than once, that's not good enough. Using j to avoid the cast is a great golf, thank you. \$\endgroup\$
– O.O.Balance
Commented Apr 19, 2018 at 14:07
\$\begingroup\$ 52 bytes. \$\endgroup\$
– Jonathan Frech
Commented Apr 19, 2018 at 20:32

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Erik the Outgolfer · Accepted Answer · 2018-11-03 18:56:09Z

1

///, 63 bytes

/b/000111//A/b1b//B/b0b//C/0BA1//X/CACACACA0bCBCBCB/0bXXCBXCAC0

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answered Nov 3, 2018 at 18:56

Erik the Outgolfer

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emanresu A · Accepted Answer · 2021-03-22 09:05:59Z

Deadfish~, 1301 bytes

{iiiii}ddccccicccdccccicccdccccicccdccciccccdccciccccdccciccccdcccicccdccccicccdccccicccdccciccccdccciccccdccciccccdcccicccdccccicccdccccicccdccciccccdccciccccdccciccccdcccicccdccccicccdccccicccdccciccccdccciccccdccciccccdcccicccdccccicccdccccicccdccccicccdccciccccdccciccccdcccicccdccccicccdccccicccdccccicccdccciccccdccciccccdcccicccdccccicccdccccicccdccccicccdccciccccdccciccccdcccicccdccccicccdccccicccdccccicccdccciccccdccciccccdccciccccdcccicccdccccicccdccccicccdccciccccdccciccccdccciccccdcccicccdccccicccdccccicccdccciccccdccciccccdccciccccdcccicccdccccicccdccccicccdccciccccdccciccccdccciccccdcccicccdccccicccdccccicccdccccicccdccciccccdccciccccdcccicccdccccicccdccccicccdccccicccdccciccccdccciccccdcccicccdccccicccdccccicccdccccicccdccciccccdccciccccdcccicccdccccicccdccccicccdccccicccdccciccccdccciccccdcccicccdccccicccdccccicccdccccicccdccciccccdccciccccdccciccccdcccicccdccccicccdccccicccdccciccccdccciccccdccciccccdcccicccdccccicccdccccicccdccciccccdccciccccdccciccccdcccicccdccccicccdccccicccdccciccccdccciccccdccciccccdcccicccdccccicccdccccicccdccccicccdccciccccdccciccccdcccicccdccccicccdccccicccdccccicccdccciccccdccciccccdcccicccdccccicccdccccicccdccccicccdccciccccdccciccccdcccicccdccccicccdccccicccdccccicccdccciccccdccciccccdccciccccdcccicccdccccicccdccccicccdccciccccdccciccccdc

Stack Exchange Network

find the pattern in this number sequence of 1's and 0's

16 Answers 16

Jelly, 11 10 bytes

How?

Ruby, 34 29 26 22 bytes

Dyalog APL, 99 83 82 bytes

Jelly, 31 bytes

How?

Java 8, 75 64 62 bytes

Wolfram Language (Mathematica), 96 bytes

Python 3, 42 bytes

JavaScript (Node.js), 41 33 bytes, port

JavaScript (Node.js), 121 bytes, original

Stax, 13 11 bytes

Z80Golf, 27 bytes

J, 17 bytes

Japt, 13 bytes

Charcoal, 13 bytes

C, 55 53 52 bytes

///, 63 bytes

Deadfish~, 1301 bytes

Your Answer

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code-golf
sequence
kolmogorov-complexity
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Hot Network Questions

find the pattern in this number sequence of 1's and 0's

16 Answers 16

Jelly, 11 10 bytes

How?

Ruby, 34 29 26 22 bytes

Dyalog APL, 99 83 82 bytes

Jelly, 31 bytes

How?

Java 8, 75 64 62 bytes

Wolfram Language (Mathematica), 96 bytes

Python 3, 42 bytes

JavaScript (Node.js), 41 33 bytes, port

JavaScript (Node.js), 121 bytes, original

Stax, 13 11 bytes

Z80Golf, 27 bytes

J, 17 bytes

Japt, 13 bytes

Charcoal, 13 bytes

C, 55 53 52 bytes

///, 63 bytes

Deadfish~, 1301 bytes

Your Answer

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Hot Network Questions

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sequence
kolmogorov-complexity
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