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Is there a way of taking a number known to limited precision (e.g. $1.644934$) and finding out an "interesting" real number (e.g. $\displaystyle\frac{\pi^2}{6}$) that's close to it?

I'm thinking of something like Sloane's Online Encyclopedia of Integer Sequences, only for real numbers.

The intended use would be: write a program to calculate an approximation to $\displaystyle\sum_{n=1}^\infty \frac{1}{n^2}$, look up the answer ("looks close to $\displaystyle\frac{\pi^2}{6}$") and then use the likely answer to help find a proof that the sum really is $\displaystyle \frac{\pi^2}{6}$.

Does such a thing exist?

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up vote 23 down vote accepted

Try Wolfram Alpha. It actually does sequences as well.

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Wow, that's... amazing. Exactly what I was after. Thank you! – Simon Nickerson Jul 21 '10 at 7:23
That is not all it does... – BlueRaja - Danny Pflughoeft Jul 26 '10 at 20:56

I've long used Simon Plouffe's inverse symbolic calculator for this purpose. It is essentially a searchable list of "interesting" numbers.

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I'd been using but your link looks like a much-updated version, thanks! – barrycarter Mar 14 '11 at 4:11

Sometimes the decimal digits of numbers will appear in Sloane's On-Line Encyclopedia of Integer Sequences OIES.

E.g. here is the decimal expansion of pi.

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