Finding More Patterns in the Perfect-Shuffle (Riffle) Integer Sequence with Wolfram-Cloud

Published: 05 August 2024
on channel: Thomas Blum

This video is a follow up of two others ( • Using Wolfram-Cloud/Mathematica to ex... and • More on the Perfect Shuffle (Riffle) ... ) in which we use Wolfram-Cloud/Mathematica to look at the integer sequence that arise from the "perfect shuffle" (riffle) scenario. If x is half the size of the deck, and y is the number of riffles to restore the original order, many of the (x, y) points fall on lines with "simple" rational slopes. By looking at the x's in various bases we find patterns for the x's of some of the points falling on some select lines with slopes like 4/3, 8/5, 20/11, 24/13 (which form a "pattern of patterns" ) and 6/7 (which is a similar pattern but is in different region in the solution graph.

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