10
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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]
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  • \$\begingroup\$ this is my first time posting a code puzzle. if you have any style improvements. let me know. \$\endgroup\$ – john mangual Apr 18 '18 at 20:41
  • 7
    \$\begingroup\$ 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. \$\endgroup\$ – Mnemonic Apr 18 '18 at 20:47
  • 3
    \$\begingroup\$ 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. \$\endgroup\$ – Mnemonic Apr 18 '18 at 20:52
  • \$\begingroup\$ @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 \$\endgroup\$ – john mangual Apr 18 '18 at 20:56
  • \$\begingroup\$ 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. \$\endgroup\$ – Magic Octopus Urn Apr 23 '18 at 0:22

14 Answers 14

17
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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.
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  • \$\begingroup\$ ah you found it \$\endgroup\$ – Jonathan Allan Apr 18 '18 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 Apr 18 '18 at 22:14
  • 6
    \$\begingroup\$ Well that's quite anticlimactic, was expecting something more intricate. \$\endgroup\$ – Nit Apr 18 '18 at 22:16
  • \$\begingroup\$ @JonathanAllan I originally tried just but apparently that's just mod 2 rather than lowest bit, so I added the to fix it. Swapped now \$\endgroup\$ – ETHproductions Apr 18 '18 at 22:21
  • 1
    \$\begingroup\$ ȷḶ×⁽q£:ȷ5Ḃ works, for 10 bytes. \$\endgroup\$ – Dennis Apr 19 '18 at 2:45
3
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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.

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3
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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.

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2
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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]          
\$\endgroup\$
  • \$\begingroup\$ I've never seen Jelly before! \$\endgroup\$ – john mangual Apr 18 '18 at 22:01
  • \$\begingroup\$ 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. \$\endgroup\$ – Jonathan Allan Apr 18 '18 at 22:03
  • \$\begingroup\$ i promise to get better at posing questions. i see there's a sandbox and some standard formatting. \$\endgroup\$ – john mangual Apr 18 '18 at 22:05
  • \$\begingroup\$ This was pretty much my approach when I started. \$\endgroup\$ – Esolanging Fruit Apr 18 '18 at 22:19
  • \$\begingroup\$ @EsolangingFruit I thought as I was doing it that it could be a fraction doing the repetition... 117/400 it seems! \$\endgroup\$ – Jonathan Allan Apr 18 '18 at 22:22
2
\$\begingroup\$

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
\$\endgroup\$
1
\$\begingroup\$

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

Thank Rick Hitchcock for 4+ bytes

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

Try it online!

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)

Try it online!

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  • \$\begingroup\$ Save 4 bytes using recursion: f=(i=0)=>i<1e3?(i*.29253&1)+f(i+1):'' \$\endgroup\$ – Rick Hitchcock Apr 19 '18 at 17:58
1
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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.

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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 Apr 18 '18 at 23:54
1
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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!

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1
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Z80Golf, 27 bytes

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

Try it online!

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.

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0
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J, 17 bytes

2|<.0.29253*i.1e3

A J port of ETHproduction's Jelly answer.

Try it online!

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0
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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.

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0
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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).

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0
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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
}
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  • \$\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 Apr 19 '18 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 Apr 19 '18 at 14:07
  • \$\begingroup\$ 52 bytes. \$\endgroup\$ – Jonathan Frech Apr 19 '18 at 20:32
0
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///, 63 bytes

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

Try it online!

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