alt Hacker NewsMy kids love taking about big numbers. TREE(3) is a family favorite. So, I was going over sequences with them, and I decided to go slow instead. My sequence was: 1 1 1 1 ... 1 ...
They accused me of using just "all 1s" (which is, naturally, cheating). Ai contraire!
The count of the number of digits in the decimal representation of the number of unique primes in the prime factorization of the natural numbers.
The best part is that even pretty young kids can compute this sequence; by the first "2" is at 2*3*5*7*11*13*17*19*23*29!
(Hopefully I got that right; the phone doesn't make it easy to type!)
I've struggled to understand how TREE(3) works and why it grows so big. I once posted to Math.Stackexchange many years ago and got a professor to help explain it to me: https://math.stackexchange.com/questions/313134/why-is-tree3...
I also loved David Metzler's series on ridiculously big numbers: https://www.youtube.com/playlist?list=PL3A50BB9C34AB36B3