A336911 Image of n under the x^3+1 map, which is a variation of the 3x+1 (Collatz) map.

0, 2, 1, 28, 2, 126, 2, 344, 2, 730, 3, 1332, 3, 2198, 3, 3376, 4, 4914, 4, 6860, 4, 9262, 4, 12168, 4, 15626, 5, 19684, 5, 24390, 5, 29792, 5, 35938, 5, 42876, 6, 50654, 6, 59320, 6, 68922, 6, 79508, 6, 91126, 6, 103824, 6, 117650, 7, 132652, 7, 148878, 7

Offset

0,2

Comments

It seems that all x^3+1 trajectories reach 1; this has been verified up to 10^10. Once a x^3+1 trajectory reaches 1, it repeats the following cycle: 1, 2, 1, 2, 1, ...

Links

Table of n, a(n) for n=0..54.

Wikipedia, Collatz conjecture

Formula

a(n) = floor(sqrt(n)) if n is even, n^3+1 if n is odd.

Example

For n = 2, a(2) = floor(sqrt(2)) = 1, because 2 is even.
For n = 5, a(5) = 3^5+1 = 126, because 5 is odd.

Prog

(Python)
from math import floor, sqrt
def a(n): return n**3 + 1 if n % 2 else int(floor(sqrt(n)))
print([a(n) for n in range(101)])
(Python)
from math import isqrt
def A336911(n): return n**3+1 if n&1 else isqrt(n) # Chai Wah Wu, Aug 04 2022

Crossrefs

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

Cf. A336912 (gives number of steps to reach 1).

Sequence in context: A138955 A089963 A362013 * A322230 A353910 A353913

Adjacent sequences: A336908 A336909 A336910 * A336912 A336913 A336914

Keyword

nonn

Author

Robert C. Lyons, Aug 07 2020

Status

approved