A Quantum Immortal

I was wondering – how many of you ever thought about the sequence 0,1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,…?

It’s a sequence that’s fun to try and recite (fun = fun for me, yeah I’m a geek I know). I just recently found out that my little sister Shira also independently “discovered” this sequence and enjoys reciting it from time to time.

Have any of you done so as well?

BTW, the lengthiest prefix of it I can quickly produce (in one or two attempts) without external aid is the first 112 elements:
0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0,

This is a cute math game I’d recommend to anyone learning addition, and in general 🙂
You shoot two’s and three’s at numbers trying to subtract from them and get exactly zero.

Rules of the Swarm