So it’s growing faster.
The Inventory Sequence was invented by Joseph Rozhenko and it goes like this: we build up a sequence and every so often pause and take an inventory of it and repeat. For example, we might start off with blank paper and ask how many 0s can you see? Zero. We then write down we have zero 0s. When we see a 0 we have to take stock again and take a new inventory. As the sequence grows, we take stock each time a 0 is encountered.
Jan Ritsema van Eck also created a plot of the first thousand terms of the sequence, which looks like a pin plot. He noticed that if you look at the upper envelope of these points, it’s about square root of 2n. However, when he plotted the first ten thousand terms, the brown line is useless as it grows much faster than square root of 2n. So that’s the challenge for today, can you find the
number of leaps for each stone on the infinite
pathway? .
If you’re looking for a challenge and have a knack for problem-solving and working with numbers, consider joining one of Jane Street’s genius teams located in Hong Kong, New York, and London. For more information, check out their website which will be linked in the video description. Have fun exploring the infinite possibilities!