# Is there a website like OEIS for real constants?

I'm hoping an online service exists where I can type in say 3.14159 and it then shows a bunch of 'interesting' (however one would define that) numbers.

Naturally in that instance it would bring up $\pi$ first as the most likely candidate, then $355/113$ then increasingly more bizarre numbers. Ideally with a weighting towards use of irrational/transcendental numbers and simplicity of expression.

I have a very messy expression that is currently graphed and I want to find out if the maximum of the graph is a known number.

Thanks in advance!

• You can search OEIS for "3, 1,4,1,5,9" and get oeis.org/A000796 – Ethan Bolker Sep 17 '17 at 18:29
• I'm more interested in the idea of a large database as that will only bring up an individual possibility, if one is known. Typing in 0.693, or 0,6,9,3 gives "The Dottie number: decimal expansion of root of cos(x) = x." Whereas I would be more interested in either $ln(2) = 0.693147180$ or $\frac{1}{3}^{\frac{1}{3}} = 0.693361$ – Ben Crossley Sep 17 '17 at 18:37
• @BenCrossley-hobbyist: oeis.org/A002162 and oeis.org/A072365 – A. Rex Sep 17 '17 at 23:35

## 4 Answers

Inverse symbolic calculator plus:

https://isc.carma.newcastle.edu.au/

• An advanced lookup for $3.141592653589793$ gives Pi, GAM(1/6)*GAM(5/6)-Pi, and Psi(1/4)-Psi(3/4) – Henry Sep 17 '17 at 18:32
• Aside from it being horrible to look at, this is perfect! Thanks a lot – Ben Crossley Sep 17 '17 at 18:41
• I tried it for Conway's constant, 1.303577269034, and it returned no results. – 6005 Sep 18 '17 at 0:02
• You have a feed it a surprising number of digits before $e$ comes towards the top of the list. I suppose this constant pops up quick frequently in math, so it has to work with tons of possible answers. – erfink Sep 18 '17 at 0:10

There is also a tool RIES - Find Algebraic Equations, Given Their Solution with the source code available.

Wolfram|Alpha (https://www.wolframalpha.com) can return an assortment of information about a decimal number including a list of possible closed forms, e.g.

https://www.wolframalpha.com/input/?i=1.303577269034

https://isc.carma.newcastle.edu.au/ did not do anything useful with this particular number.

This is not really what you want. But a method that you can try is the lowest denominator method.

How this works is you have a value $\alpha$ and a margin $\epsilon$.

You then return the value of the form $\frac{mc}{n}$ inside $(\alpha-\epsilon,\alpha+\epsilon)$ that minimizes $n$. Here you take $c$ inside a set of constants, a preliminary set could be $\{1,\pi,e,\pi^{-1},e^{-1}\}$

• That's a nice method if you expect the answer to be "nice". The problem here is that the constants coming up in my work could be anything. They may just be meaningless transcendentals and writing them in terms of familiar symbols may not be possible. – Ben Crossley Sep 17 '17 at 18:44