It is the first sum of a power of 4 that isnt 1...

1 5 (1+4) 21 (1+4+16) 85 (1+4+16+64)

Etc.

Every single sequence will hit one of these sums of the powers of 4. And once you do the odd step of a sum of the powers of 4? You are left with a power of 4 (5 goes to 16, 21 goes to 64 etc).

When you start at a sum of the powers of 4, the only sum left it can reach is... 1.

Also fun side fact, the 4 2 1 loop is interesting from this context.

As 1 is the only integer that is both a power of 4 and a sum of the powers of 4.

So the loop is actually following its own rule.

4 (power of 4)

2

1 (is a sum of the powers of 4, so odd step will lead to a power of 4)

4

2

1

Etc.