A279909 Number of steps to reach 1 or a cycle in the Collatz-like problem '3x/2' and '(x-1)/2'.

0, 2, 1, 3, 3, 3, 2, 8, 3, 4, 4, 7, 4, 6, 3, 11, 9, 6, 4, 15, 5, 12, 5, 11, 8, 6, 5, 7, 7, 14, 4, 18, 11, 10, 10, 11, 7, 9, 5, 11, 16, 6, 6, 15, 13, 12, 6, 17, 12, 9, 9, 11, 7, 11, 6, 19, 8, 8, 8, 11, 15, 14, 5, 24, 19, 14, 11, 13, 11, 13, 11, 16, 12, 8, 8, 10, 10, 10, 6, 16, 11, 17, 17, 18, 7, 26, 7, 24, 16, 11, 14, 13, 13, 15, 7, 23, 18, 14, 13, 23

Offset: 1

Author

Luca Petrone, Apr 11 2017

Keywords

• nonn
• easy

Comments

This Collatz-like problem is as follows: start with any number n. If n is even, divide it by 2 and multiply by 3, otherwise subtract 1 and divide it by 2.

The iteration always reach {1} or the cycles {4, 6, 9} and {16 , 24 , 36 , 54 , 81 , 40 , 60 , 90 , 135 , 67 , 33}.

Links

• Luca Petrone, Table of n, a(n) for n = 1..19999
• Luca Petrone, Log Plot for the first million terms

Crossrefs

Cf. A006577.

Programs

Python

def a(n):
    if n==1: return 0
    l=[n]
    while True:
        if n%2==0: n=(n//2)*3
        else: n = (n - 1)//2
        if not n in l:
            l+=[n]
            if n<2: break
        else: break
    if l[-1]==1: return len(l)-1
    return len(l)
for n in range(1, 20001):
    print(n, a(n)) # Indranil Ghosh, Apr 13 2017