

A336911


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


1



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
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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)])


CROSSREFS

Cf. A006370 (image of n under the 3x+1 map).
Cf. A336912 (gives number of steps to reach 1).
Sequence in context: A235031 A138955 A089963 * A322230 A012411 A012415
Adjacent sequences: A336908 A336909 A336910 * A336912 A336913 A336914


KEYWORD

nonn


AUTHOR

Robert C. Lyons, Aug 07 2020


STATUS

approved



