Is there a real number lookup algorithm or service?

Question

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?

score 25 · Answer 1 · edited Mar 22 '22 at 10:35

25

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

Edit: link updated (Mar 2022).

edited Mar 22 '22 at 10:35

DIVVS IVLIVS

13

answered Jul 21 '10 at 12:42

Michael Lugo

24,422

1

I'd been using http://pi.lacim.uqam.ca/eng/ but your link looks like a much-updated version, thanks! – Mar 14 '11 at 04:11
The link seems to be down. So I created an alternative using Robert Munafo's RIES: https://thomasahle.com/ries – Thomas Ahle Feb 26 '25 at 13:05

score 24 · Accepted Answer · answered Jul 21 '10 at 06:34

24

Try Wolfram Alpha. It actually does sequences as well.

answered Jul 21 '10 at 06:34

Casebash

9,437

1

Wow, that's... amazing. Exactly what I was after. Thank you! – Simon Nickerson Jul 21 '10 at 07:23
2

That is not all it does... – BlueRaja - Danny Pflughoeft Jul 26 '10 at 20:56

score 6 · Answer 3 · edited Feb 20 '19 at 14:08

6

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.

edited Feb 20 '19 at 14:08

Martin Sleziak

56,060

answered Jul 21 '10 at 07:26

Douglas S. Stones

21,396

Is there a real number lookup algorithm or service?

3 Answers3

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