OFFSET
1,3
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.
LINKS
Wikipedia, Collatz conjecture
EXAMPLE
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.
PROG
(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)])
CROSSREFS
KEYWORD
nonn
AUTHOR
Robert C. Lyons, Aug 08 2020
STATUS
approved