A336914 Number of steps to reach 1 in '3^x+1' problem (a variation of the Collatz problem), or -1 if 1 is never reached.

0, 1, 4, 2, 11, 2, 9, 5, 7, 5, 7, 5, 5, 5, 16, 3, 5, 3, 5, 3, 16, 3, 14, 3, 9, 3, 14, 3, 9, 3, 9, 12, 14, 12, 22, 12, 14, 12, 7, 12, 5, 12, 5, 12, 7, 12, 5, 12, 7, 12, 5, 12, 5, 12, 20, 12, 5, 12, 16, 12, 5, 12, 14, 3, 12, 3, 5, 3, 14, 3, 5, 3, 14, 3, 5, 3, 5

Offset: 1

Author

Robert C. Lyons, Aug 08 2020

Keywords

• nonn

Comments

The 3^x+1 map, which is a variation of the 3x+1 (Collatz) map, is defined for x >= 1 as follows: if x is odd, then map x to 3^x+1; otherwise, map x to floor(log_2(x)).

It seems that all 3^x+1 trajectories reach 1; this has been verified up to 10^9.

Examples

			For n = 5, a(5) = 11, because there are 11 steps from 5 to 1 in the following trajectory for 5: 5, 244, 7, 2188, 11, 177148, 17, 129140164, 26, 4, 2, 1.
For n = 6, a(6) = 2, because there are 2 steps from 6 to 1 in the following trajectory for 6: 6, 2, 1.
		

Links

• Wikipedia, Collatz conjecture

Crossrefs

Cf. A006370 (image of n under the 3x+1 map).

Cf. A336913 (image of n under the 3^x+1 map).

Programs

Python

from math import floor, log
def a(n):
    if n == 1: return 0
    count = 0
    while True:
        if n % 2: n = 3**n + 1
        else: n = int(floor(log(n, 2)))
        count += 1
        if n == 1: break
    return count
print([a(n) for n in range(1, 101)])