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Oct 16, 2017 at 22:46 comment added Gerry Myerson It might be fun to do some experiments here. Take some such algebraic irrational, maybe $\sqrt2-1$, apply your operation to it, and then feed the result into the Inverse Symbolic Calculator or into an integer-relation finder like PSLQ, and see whether anything interesting comes out.
Oct 16, 2017 at 18:45 comment added Loïc Teyssier Ok, only to check (though I guess it wouldn't make the question any easier).
Oct 16, 2017 at 18:43 comment added orangeskid @Loïc Teyssier: Correct, what is written down.
Oct 16, 2017 at 18:35 comment added Wojowu Most likely the answer is not known...
Oct 16, 2017 at 18:34 comment added Loïc Teyssier Do you really mean what you've just written down, or $\sum_{n\geq 1}\frac{a_{2n}}{2^{2n}}$ ?
Oct 16, 2017 at 17:18 history asked orangeskid CC BY-SA 3.0