[seqfan] Re: Powers of Two in Base Three

[Robert Gerbicz]

Hi!

2^k=sum(i=0,L,a(i)*3^i) then sum(i=0,L,a[i])==0 mod 2
so there should be even number of ones for k>0.

Hans Havermann <gladhobo at bell.net> ezt írta (időpont: 2020. máj. 6., Sze,
15:59):

> 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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