[seqfan] Re: Pi Day Question
elvis at graceland.math.uwaterloo.ca
Sun Mar 15 00:45:44 CET 2009
> I believe that the number
> 0.12345678910111213141516171819202122232425262727293-031.. . .
> was proved to be normal many, many years ago. I heard a rumor fifty-two
> ago via my number theory teacher, the late Alfred T. Brauer (at Univ. of
> that perhaps a Russian mathematician had proved that the number
> 0.23571113171923293137 . . . formed by joxtaposing the digits of the prime
> number sequence, is normal; however I do not recall finding a reference.
> Can any Sequence Fanatic answer this and can anyone cite other specific
> which are normal?
Champernowne's number .12345678910... is normal to base 10, but not known
to be normal in other bases. See Champernowne, J. London Math. Soc.
The number .23571113171923.... was proved normal in base 10
by Copeland and Erdos, Bull Amer. math. Soc. 52 (1946), 857-860, but it is
not known to be normal in other bases.
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