# A puzzling data-driven sequence

First puzzle! I was inspired by this question to make my own. Props to the author for itching my brain!

Update: I double-checked the sequence, turns out it changed! I overlooked something which I have now made a note of in Hint 3. You are now trying to find the 13th number instead of the 14th.

Update 2: Updated the sequence again.

What is $x$ in this sequence?

$3,1,203,3,1,1,0,4,4,2,1,0,x,0,...$

This can be solved using only information that is found on Puzzling.SE.

Hint:

Think about the linked question. This sequence can be solved in a similar way.

Hint 2:

This sequence also changes, but not as often as the linked question.

Hint 3:

The bigger numbers change more often than the smaller ones.

Key Hint (updated):

3 digits, 2 numbers, 1 op. All-time high.

Key Hint 2 (updated):

There is a code hidden in the Puzzling.SE link.

Key Hint 3:

All the information can be found on a single list of users on a single page.

Key Hint 4 (final?):

Integer division is involved. The code from Key Hint 2 describes the operation.

• When it changes, is the change significant? Jun 9 '16 at 22:19
• The maximum change I would expect at one time would be two numbers swapping places, or one number increasing or decreasing by 1. Jun 10 '16 at 4:08
• I would say the list represents the upvotes for the questions or answers of one of the users on Puzling SE. I'm trying to find who it is. Jun 10 '16 at 14:04
• Oh... check the puzzling link? You're referring anti-cache? What's with it :/ Jun 10 '16 at 16:25
• Any experienced puzzler should be able to see that the link is base64 for "rep divide", I don't think you needed to give more hints about that.
– ffao
Jun 10 '16 at 19:38

Due to my misunderstanding of how difficult this puzzle actually is, and by recommendation of other users active here, I've decided to answer it myself. Hopefully this will illustrate my train of thought as I built it.

The sequence is from

the list of Puzzling.SE users with all-time highest reputation, found here: https://puzzling.stackexchange.com/users?tab=Reputation&filter=all The image above is slightly modified. I expanded the rep for each of the users so you see 31758 instead of 31.7k, as well as appended the ID for each user next to their name. The concept is the same.

To find the sequence,

take the list of users in order, starting from the one with the highest rep. Divide each user's reputation by their ID, discarding the decimal.

For the first user (Gamow), the calculation would be $31758 / 8874 = \lfloor3.578769...\rfloor = 3$.
Second (f''): $24004 / 12408 = \lfloor1.934558...\rfloor = 1$.
Third (Joe Z.): $17867 / 88 = \lfloor203.034090...\rfloor = 203$.

Following this pattern, the 13th member of the sequence can be found:
$9032 / 28 = \lfloor322.571428...\rfloor = 322$.

Thus, $x$ is $322$.

Explanation of key hints:

3 digits, 2 numbers, 1 op. All-time high. The answer has three digits, which can be found using two numbers and one mathematical operation (dividing reputation by the ID of all-time high reputation users).

There is a code hidden in the Puzzling.SE link. The Base64-encoded string at the end of the link decodes to repdivid, or rep div id (reputation divide ID).

All the information can be found on a single list of users on a single page. The snapshot of the page above makes the necessary information obvious, but the exact reputation can be found without modifying the page by hovering the rep count of a user. The ID can be found by hovering the user's link and noting the number in the address.

Integer division is involved. The code from Key Hint 2 describes the operation. This is a directive to drop the decimal place of each calculation to find the correct sequence member.

• [+1] very nice indeed. . Jun 11 '16 at 18:43
• I wonder if we can sort users by "reputation / ID number". klm123 is higher than me, but Kevin is higher than both of us.
– user88
Jun 12 '16 at 1:31
• Wow I was so close...I was dividing Reputation by the number of posts for each all-time high user...forgot to think outside of the box. Also, the fact that your Base64 code spelled "repdivid" and not "repdivide" had me going on some wild goose chase lol... Jun 12 '16 at 5:30
• Huh, this was really difficult... Jun 12 '16 at 10:26
• @nicael That's on me. I'm working in a new (different) puzzle, hopefully will be more straightforward and fun. :) Jun 13 '16 at 13:33

So I can't comment yet, so I'll post what I've tried (and a question to OP)

Basically, I've mostly tried doing stuff on this nifty page, which allows you to query data on Puzzling using SQL. I've tried relating (all with regards to Puzzling SE):

• Reputation for a user