

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.


1



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
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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(log2(x)).
It seems that all 3^x+1 trajectories reach 1; this has been verified up to 10^9.


LINKS

Table of n, a(n) for n=1..77.
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

Cf. A006370 (image of n under the 3x+1 map).
Cf. A336913 (image of n under the 3^x+1 map).
Sequence in context: A135440 A215500 A188128 * A091484 A163544 A191728
Adjacent sequences: A336911 A336912 A336913 * A336915 A336916 A336917


KEYWORD

nonn


AUTHOR

Robert C. Lyons, Aug 08 2020


STATUS

approved



