# Two James Tanton Questions

It’s midterm week at school, and James Tanton threw out two interesting questions in two days. I spent a little time programming “solutions” to these problems (not solutions, just verifications for an infinitesimally small portion of the natural numbers).

## Problem One:

Here’s my processing.org code for this problem. And here’s the output of the code, each time the sequence gets longer, it prints out the new “max” sequence length.

I didn’t use any of processing.org’s graphics but I had the prime function optimized, so it was quick work.

## Problem Two:

Here’s the python code for the “solution”. And here’s the last six lines of the output of the code. I checked all numbers under 1,000,000, and all the sequences were finite (they stopped at a multiple of 13). The starting number whose sequence ended in the largest multiple of 13 was 964,665, and the multiple of 13 had 384 digits (BIG NUMBER! There are only ~10^80 particles in the entire universe). Fun stuff.

[Edit: 1/28/2014 9:08am] Ok, ok. James asked for a proof for the second problem. Here you go ๐

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