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Experimental Mathematics Seminar

Eric Angelini's Comma Sequence Part 2

Natasha Ter-Saakov, Rutgers University

Location:  https://rutgers.zoom.us/j/94346444480 [password: The 20th Catalan number, alias (40)!/(20!*21!)
Date & time: Thursday, 11 April 2024 at 5:00PM - 6:00PM

At the beginning of the semester, Neil Sloane introduced the comma sequence (introduced to him by Eric Angelini) that works as follows. Choose your favorite number in your favorite base. Now we'll build a sequence from it with the following rule: the difference between consecutive terms is equal to the concatenation of the digits on either side of the comma between them. If you chose 1 and base 10, then your next terms would be 12 because 12-1=11 and then 35 because 35-12=23. This sequence will continue for 2,137,452 steps, then fails to find a suitable successor for the value 99,999,945. We will discuss some problems presented by Sloane including a proof that all comma sequences in bases 3 through 19 are finite. Based on joint work with Robert Dougherty-Bliss.

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