2
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Here is another number sequence riddle for you all:

4, 2, 7, 6, 8, __, __, and so on. What numbers go in the blanks?

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    $\begingroup$ I mean, there's oeis.org/A245262, but I don't think that's it :P $\endgroup$ – Zimonze Feb 10 at 23:39
8
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The sequence continues

6,3,3,3

and terminates there because

the numbers are the lengths of the words in the question. (I have taken the view that the sequence stops where the numbers begin rather than, e.g., spelling the numbers out in words and using their lengths.)

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    $\begingroup$ But it would certainly be fun to come up with a puzzle based on the same principle and also matching the A245262 to 15 digits or so... :-) $\endgroup$ – kkm Feb 11 at 1:09
2
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The blanks stand for

6, 6

because this is

the beginning of the decimal expansion of the absolute value of the Dawson integral at the extrema inflection points [many thanks to @GarethMcCaughan for noticing the error], ±0.4276866160179287974... (there are two of them, symmetric about the origin). See OEIS entry A245262.

Ah, aren't number sequence puzzles fun! ;-)

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  • $\begingroup$ You might want to credit @Zimonze in your answer. $\endgroup$ – Brandon_J Feb 10 at 23:44
  • $\begingroup$ Of course, my answer is tongue-in-check. Any "missing number" puzzle has an infinite number of solutions. $\endgroup$ – kkm Feb 10 at 23:45
  • $\begingroup$ Oops. Didn't see that. $\endgroup$ – Brandon_J Feb 10 at 23:45
  • $\begingroup$ @Brandon_J, ah, great minds do think alike!!! The timing is just a few seconds apart. I am not assuming you are accusing me of plagiarism? Solving puzzles was supposed to be fun, and that would be quite the opposite. I do indeed respect Zimonze addressing the OEIS, but I would be really surprised if anyone would not do the same upon reading the question... So the fairest credit indeed belongs do Dr. Sloane, I believe. Anyway, my answer was intended as a joke. $\endgroup$ – kkm Feb 10 at 23:52
  • $\begingroup$ No, definitely not plagiarism, since he didn't actually invent the sequence. I was just saying that since he came in three minutes before you it might be nice to give him a shout-out, especially if you saw his answer/comment before posting yours (which it appears you did not). All good! $\endgroup$ – Brandon_J Feb 10 at 23:54

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