[Interesting](https://math.stackexchange.com/questions/2297901/a-conjectured-mathematical-constant-for-base-10-normal-numbers) rational constant concerning base-10 normal numbers. 

>Let $a$ be a real number with a base - 10 decimal
> representation $a_1a_2\ldots a_n \ldots$ Denote the number of ways to
> write $a_n$ as the sum of positive integers as $p(a_n)$ - also called
> the [partition](https://en.wikipedia.org/wiki/Partition_(number_theory))
> of $a_n$. I write  $$\beta(a)=\sum_{n=1}^{\infty}{p\left(a_n\right)\above 1.1pt a_n}$$ 
> If $a$ is a base-10 normal number then $\beta(a)={97 \above 1.5 pt 45}$. 

Note the converse of the above statement is false! 

Numerically ${97\above 1.5pt 45}$ can be written $2.15\ldots$.  If we believe $\pi$ is normal then we would expect $\beta(\pi)={97 \above 1.5 pt 45}$. Up to the $500\text{ }000$-th digit $\beta(\pi)=2.153781\ldots$