It seems like there's been a constant flow of new, and mostly questionable, number sequence puzzles popping up on the site recently. My turn to add to the proverbial three-ring circus!

$0, 9, 5, 1, 6, 0, 1, 15, 2, 17, 21, 4, ...$

What are the next $3$ values in this series?


Now I know many of these have been roundly panned for being Bad Puzzles™—some even by me—so before anyone reaches for the down-vote, flag or vote-to-close buttons, rest assured that I know What Not To Do in a Number Sequence Puzzle. I've been circumspect in creating this sequence puzzle, and believe it is solvable, uniquely, given what I've provided here. Have fun!




helpfulness level 0:

Technically, this could be solved by analyzing the numbers alone; but it's highly unlikely. So there are clues provided in the text. (The link to What Not To Do was not gratuitous.)

helpfulness level 1:

@wildBillMunson and @DrnglVrgs have provided some highly relevant hints of their own.

helpfulness level 2:

The title is completely irrelevant. The text is not: there's a fundamental part of the puzzle "hiding" right out in the open.

helpfulness level 3:

Related? Two pieces of chocolate pie

helpfulness level 4:

Similar...   $\text{O E I S A 0 0 1 2 2 3}$

  • 1
    $\begingroup$ Can this be solved by analyzing the numbers alone, or are there necessary clues provided in the text? $\endgroup$ Jan 15, 2017 at 2:11
  • 4
    $\begingroup$ @wildBillMunson That's a very good question. :) $\endgroup$
    – Rubio
    Jan 15, 2017 at 2:24
  • $\begingroup$ Does the edit change the values? $\endgroup$
    – Herb
    Jan 15, 2017 at 19:56
  • $\begingroup$ @HerbWolfe No, or I would have reverted it. $\endgroup$
    – Rubio
    Jan 15, 2017 at 19:57
  • 1
    $\begingroup$ I noticed you've used the words 'ring', 'roundly', and 'circumspect', all of which seem to indicate some kind of circular pattern. This seems to be the kind of well-embedded clue that you're known for... ;) $\endgroup$ Jan 18, 2017 at 8:12

2 Answers 2


The next 3 values are :

19, 3, 7

Why ?

Because the clues noticed by @wildBillMunson guided me on the way to Pi, which you confirmed with the 4th clue (and answer to @DrnglVrgs). Furthermore, the number three (3) appeared twice in the context, so it seemed to be important. (And it's been 27 days this question has been asked, as 27 = 3^3, this is ... oh, sorry, totally coincidental ;) )

So, how exactly ?

I looked up in the decimal expansion of Pi the occurrences of 3, looking for anything good. It happened to me that the sequence number you provided is the number of symbols (and not digits because either I am totally wrong or the dot counts) between each of those occurrences of 3. Because I'm lazy, I got the pi sequence from this website and wrote this little Python code to extract the next three digits.

  • $\begingroup$ Just so - nicely done! $\endgroup$
    – Rubio
    Feb 11, 2017 at 23:07

This answer should be at least 33% correct


The wild and probably wrong process:

Divide the series in sets of three
The treat the columns separatedly, the middle one was the first:
9+6=15 15+6=21 21+15=36
the first column I followed the link you provided and arrived here
The last column was searching in the digits of pi (because you said circle a lot)

  • 1
    $\begingroup$ There's a single sequence here, not a union of radically different series formations. Nonetheless, at least 33% of your basic concepts were correct (though the specifics of what you did don't seem to be). $\endgroup$
    – Rubio
    Jan 25, 2017 at 17:15
  • $\begingroup$ Interesting, thank you, will continue $\endgroup$
    – DrnglVrgs
    Jan 25, 2017 at 17:17

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