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Q-Toothpick sequence

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GuyBarry
1299281.  Wed Oct 17, 2018 12:37 pm Reply with quote

Something for the "Q series" and the New Number Fact Game as well:

The 50th Q-toothpick number is 5126.

On an infinite square grid, draw a quarter circle from one corner of a square to the opposite corner of that square.
Call an endpoint of a quarter circle (or a “Q-toothpick”) exposed if it does not touch the endpoint of any other quarter circle.
From each exposed endpoint, draw two more quarter circles, each of the same size as the first quarter circle you drew. Furthermore, the two quarter circles that you draw are the ones that can be drawn “smoothly”.

Here's how it unfolds.

The total number of Q-toothpicks present in the nth generation is here.

 

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