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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 ...

Notice that even though output is in a log scale, output is shooting up in an exponential way. DATA from Brad DeLong