[jurassicfoxy]

I previously memorized pi to 100 decimals. Was fun, and now I'll never forget 3.1415926535897932384626433 ... how many is that? 25?

There are a several little triplet "patterns" in this first batch that make it easy to this point:

3.1415 926 535 8 979 323 84 626 433.

[FredPret]

I'm guessing the answer to this question is no, but... for an irrational number like pi, can we guarantee that a certain digit sequence will occur somewhere in its infinite reaches?

That would be a wildly impractical but very fun way to encode information - if everybody had a couple of petabytes of pi on their harddrive one day, you could just send the starting and ending digit to communicate an arbitrary amount of information this way.

Of course you'd first have to search through the whole universe of digits to find a sequence that's just right.

[Arnavion]

Such numbers are called "normal numbers". Pi likely is one based on all the digits we've computed for it, but we don't have any way to prove a given number like pi is normal or not.

Relevant Numberphile video: https://www.youtube.com/watch?v=5TkIe60y2GI

[FredPret]

Very interesting, thank you. He starts talking about this at 8:20

[thfuran]

1.01001000100001... is infinite and non-repeating, but doesn't contain all substrings. A number that does is called a "normal" number, and it's not known whether pi is. It seems to be pretty normal though.

[kurisufag]

this in practice: https://github.com/ajeetdsouza/pifs

[bitwize]

That reminds me of how on The IT Crowd, the new -- exceedingly long -- Emergency Services number replacing 999 was fairly easy for Moss to remember. Being divided into groups of at most 5 digits probably helped.