Benford's Law and the OEIS

[Simon Nickerson]

On Wed, 24 Aug 2005, Alonso Del Arte wrote:
> I'm wondering if anyone has studied Benford's Law in connection with
> the OEIS?

As I understand it, Benford's Law is a statement about the distribution of
the most significant digit of numbers, rather than all their digits. Thus
it is not surprising that the first 1000 digits of pi give an
approximately uniform distribution for the digits 0-9: almost all real
numbers have this property. If, however, you were to make a list of
"significant mathematical constants" and write down their first non-zero
digits, Benford's Law would predict that the digit 1 occurred about 30% of
the time. (The Mathworld article [1] on Benford's Law notes that this is
indeed the case for the large collection of mathematical constants
included in Plouffe's Inverse Symbolic Calculator.)

[1] http://mathworld.wolfram.com/BenfordsLaw.html

-- 
| Simon Nickerson            http://web.mat.bham.ac.uk/S.Nickerson
| simonn at maths.bham.ac.uk                    School of Mathematics
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