What is the shortest way to write the number $1234567890$?

Question

Here's a challenge : find the shortest way to write the number $1234567890$ .

There is several ways to write the number $1234567890$ :

• $1.23456789 × 10^9$
• $2×3^2×5×3607×3803$
• $617283945×2$

But all these notations are longer. Can you find a shorter notation than $1234567890$ ?

EDIT : For this question, the length of a notation is given by the number of characters used to write the notation on a sheet of paper.

eg : $2×3^2×5×3607×3803$ is 16 chars long.

Answer 1

How about: $\displaystyle\sum_{i=1}^{9}i\;10^{10-i}$

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Alternatively, how about $123\cdots90$? It's only $8$ characters long!

(or the $7$ character $12\cdots90$ if you find the pattern unambiguous enough)

Answer 2

What about $KF12OI_{36}$? If it were possible you could go up to base $99$, but as far as I know it's defined only for bases up until $36$.

Answer 3

In base 32 it is $14PC0MI_{32}$ (9 digits together with the base, 1 shorter than the original)

Answer 4

I stated this in a comment, so I might as well put it here. In the commonly accepted base64 notation (http://en.wikipedia.org/wiki/Base64), $1234567890 = BJlgLS_{64}$. 8 characters.

Answer 5

$$\quad\quad\quad$$




$$\tiny{1234567890}$$

Answer 6

I don't know if this is acceptable, I've been working on an algorithm to find the numerical equivalence of any sequence given a dictionary.

This is the java code for this: https://github.com/volkovasystems/convert-to-sequence.git

Now by feeding this the following inputs:

1. the sequence index: 1234567890
2. the dictionary: abcdefghijklmnopqrstuvwxyz

You can get the sequence equivalence of 1234567890 from the given dictionary which is: "jvqowyc"

You can even make it shorter or longer depending on the given dictionary.

Answer 7

It should be $$ 10 $$ in base $1234567890$ of course.