A280929 Number of steps required to reach the first prime when starting from n in the Collatz (or '3x+1') problem.

2, 3, 2, 1, 4, 1, 2, 2, 3, 1, 2, 2, 4, 1, 2, 3, 3, 4, 2, 2, 6, 1, 4, 3, 3, 1, 2, 2, 4, 3, 2, 4, 6, 1, 2, 5, 5, 1, 2, 3, 3, 7, 8, 2, 4, 1, 2, 4, 3, 4, 6, 2, 6, 3, 2, 3, 3, 1, 2, 4, 4, 1, 17, 5, 6, 7, 2, 2, 5, 3, 2, 6, 5, 1, 2, 2, 4, 3, 4, 4, 3, 1, 6, 8, 8, 1, 2, 3, 3, 5, 2, 2, 6, 1, 15, 5, 3, 4, 2, 5

Offset: 1

Author

Dmitry Kamenetsky, Jan 11 2017

Keywords

• nonn

Comments

If n=p*2^k, where k>0 and p is some prime then a(n)=k.

If n is odd then a(n)=a(3n+1)+1.

If n is even then a(n)=1 or a(n)=a(n/2)+1.

If n is composite then a(n)=A274472(n).

Examples

			The Collatz iteration for 33 is 100, 50, 25, 76, 38, 19, 58, 29, ... 1. The first prime (19) is reached after 6 steps, so a(33)=6.
		

Links

• Dmitry Kamenetsky, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A006577, A274472.