Here’s the distribution of the first million digits of the square root of two’s decimal expansion.
Number of digits | is:
0's | 99 818
1's | 98 926
2's | 100 442
3's | 100 191
4's | 100 031
5's | 100 059
6's | 99 885
7's | 100 012
8's | 100 347
9's | 100 126
If each digit had a Bernoulli chance of coming up (like a 10-sided die), you’d expect to see 10 000 ± 30 times. And going on with that same assumption, the chance of the least-frequent digit coming up less than 99 000 times would be something like one percent.
What does it mean? I will meditate on this and expand √2 in different bases besides 10.
