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A336912 Number of steps to reach 1 in the 'x^3+1' problem (a variation of the Collatz problem), or -1 if 1 is never reached. 1
0, 1, 9, 2, 7, 2, 5, 2, 10, 10, 5, 10, 5, 10, 8, 3, 5, 3, 13, 3, 13, 3, 13, 3, 16, 8, 8, 8, 13, 8, 8, 8, 11, 8, 11, 3, 26, 3, 21, 3, 6, 3, 8, 3, 8, 3, 8, 3, 16, 6, 16, 6, 16, 6, 16, 6, 6, 6, 16, 6, 16, 6, 6, 3, 6, 3, 16, 3, 21, 3, 6, 3, 11, 3, 11, 3, 29, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

The x^3+1 map, which is a variation of the 3x+1 (Collatz) map, is defined for x >= 0 as follows: if x is odd, then map x to x^3+1; otherwise, map x to floor(sqrt(x)).

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

LINKS

Table of n, a(n) for n=1..78.

Wikipedia, Collatz conjecture

EXAMPLE

For n = 3, a(3) = 9, because there are 9 steps from 3 to 1 in the following trajectory for 3: 3, 28, 5, 126, 11, 1332, 36, 6, 2, 1.

For n = 4, a(4) = 2, because there are 2 steps from 4 to 1 in the following trajectory for 4: 4, 2, 1.

PROG

(Python)

from math import floor, sqrt

def a(n):

    if n == 1: return 0

    count = 0

    while True:

        if (n % 2) == 0: n = int(floor(sqrt(n)))

        else: n = n**3 + 1

        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. A336911 (image of n under the x^3+1 map).

Sequence in context: A224268 A019877 A252898 * A010537 A234371 A172423

Adjacent sequences:  A336909 A336910 A336911 * A336913 A336914 A336915

KEYWORD

nonn

AUTHOR

Robert C. Lyons, Aug 07 2020

STATUS

approved

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Last modified July 27 15:49 EDT 2021. Contains 346308 sequences. (Running on oeis4.)