[seqfan] Re: Powers of Two in Base Three

Tim Peters tim.peters at gmail.com
Wed May 6 17:11:08 CEST 2020

Since 3 is congruent to 1 modulo 2, 3^i is also congruent to 1 modulo
2 for i >= 0.  So the parity of an integer in base 3 notation is equal
to the parity of the sum of the base 3 digits, which is equal to the
parity of the number of "1" digits.  So it's not just powers of 2, but
_all_ even integers that have an even number of "1" digits in base 3.

On Wed, May 6, 2020 at 8:59 AM Hans Havermann <gladhobo at bell.net> wrote:
> After recently extending A305942, I was curious about the digit distribution of powers of two in other normal bases. By 'normal' I mean to exclude bases two, four, and eight, where I do not expect a roughly equidistribution of digits. In base three, unexpectedly, I noticed that a count of the digit 'one' (powers > 0) is always an even number. Why?

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