Biquanimous numbers
David W. Wilson
wilson at aprisma.com
Tue Oct 9 16:19:28 CEST 2001
Bill Thurston: Thanks for your detailed discussion of this problem I
presented. My viscera are vindicated. I think I understand the crux
of the argument, but there are some details that I don't quite understand.
Right now, I have other things to do (they expect me to do work here),
but I will take this subject up with you some other time in order to
fully understand the FA construction.
Others: Thanks for your replies. The biquanimous numbers (base 2 thru 10)
should be EIS sequences, I think (I don't have time to generate them right
now). Also, I wanted to count the biquanimous numbers of various lengths,
out of curiosity. I suspect that in the limit, 1/2 of the base-b numbers
are biquanimous, which could be proved or disproved from the FA construction.
My viscera are acting up again... I suspect that in the limit, half of
the base-b numbers are biquanimous. I can prove this true of bases 2
and 3. The quick statistacal argument: Half the numbers have odd digit
sum, hence are non-biquanimous. The remaining half have even digit sum,
a long random one of these would very likely split into two same-sum
pieces, hence almost all of these are biquanimous.
- Dave Wilson
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