Here is another number sequence riddle for you all:
4, 2, 7, 6, 8, __, __, and so on. What numbers go in the blanks?
The blanks stand for
because this is
the beginning of the decimal expansion of the absolute value of the Dawson integral at the
extremainflection 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! ;-)