Previous video sets this up: https://www.youtube.com/watch?v=-ruC5A9EzzE Extra on concatenation: https://www.youtube.com/watch?v=LgnoYsbI7Uc More links & stuff in full description below ↓↓↓ We appreciate any help on Patreon - it lets us make a few more and better videos: http://www.patreon.com/numberphile Matt Parker on Numberphile playlist: http://bit.ly/Matt_Videos Matt's channel: http://bit.ly/StandUpMaths Parker Square T-Shirt: http://bit.ly/ParkerSquareTshirt Inder J. Taneja papers... Single Digit Representations of Natural Numbers https://arxiv.org/abs/1502.03501 Crazy Sequential Representation: Numbers from 0 to 11111 in terms of Increasing and Decreasing Orders of 1 to 9 https://arxiv.org/abs/1302.1479 Videos by Brady Haran Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile We are also supported by Science Sandbox, a Simons Foundation initiative dedicated to engaging everyone with the process of science. NUMBERPHILE Website: http://www.numberphile.com/ Numberphile on Facebook: http://www.facebook.com/numberphile Numberphile tweets: https://twitter.com/numberphile Subscribe: http://bit.ly/Numberphile_Sub Brady's videos subreddit: http://www.reddit.com/r/BradyHaran/ Brady's latest videos across all channels: http://www.bradyharanblog.com/ Sign up for (occasional) emails: http://eepurl.com/YdjL9