[seqfan] Re: Powers of Two in Base Three

Hans Havermann gladhobo at bell.net
Wed May 6 17:19:36 CEST 2020

Thank you, Robert and Jack, for those explanations. The solution dawned on me (of course) only after I posted. I was in the process of looking for powers of two that contained exactly n copies of digit d that I encountered this. More precisely, I was looking for an n that had no powers of two where the digit d appeared exactly n times. In base ten, such an n is too large for me to compute. (The smallest number of powers I have is *eight* for the digit 7 appearing exactly 275923 times.)  In base five, there are no powers of two (for example) where the digit 3 appears exactly 20848 times.

Because of the preponderance of solutions in base three, one may combine results for individual digits therein and say that there are no powers of two where the digit count of *any* of the three digits is 6855, to cite the smallest example.

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