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David Radcliffe

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### David Radcliffe

Shared publicly -I wrote a blog post discussing a question of Kurt Mahler: Which squares have only the digits 0 or 1 when written in base 5? I found all such squares less than 5^64 and proved that infinitely many are not divisible by 5.

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### David Radcliffe

Shared publicly -This is a directed graph with 1000 vertices, numbered from 0 to 999, and a directed edge from vertex n to vertex (n*n+2) mod 1000 for each n. I think it's rather pretty.

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Thanks for the invite; some good stuff here! Bill

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### David Radcliffe

Shared publicly -What can we say about the patterns of leading digits of (2^n, 3^n, ..., 9^n)? My answer is here.

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### David Radcliffe

Shared publicly -Do the frequencies of Emoji characters follow Zipf's law?

Emojitracker.com is a very interesting site that tracks how often each emoji is used on Twitter. The statistics are updated in real time, and it's really quite amazing to watch. (In case the reader...

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### David Radcliffe

Shared publicly -I am investigating the sum of digits of 2^n. I have discovered an elementary proof that s(2^n) > log_4 n for all n. What is the best known lower bound for this sequence?

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Ah. In that case, I have discovered an elementary proof that s(2^n) is bounded.

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Introduction

I am a college math instructor living in St. Paul MN. I am not a vice president at Google; that is a different David Radcliffe. I did not star in the Harry Potter movies; that is Daniel Radcliffe.

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