A384713 The number of steps that n requires to reach 1 under the map: x-> x^2 - 1 if x is an odd prime, x/2 if x is even, x - lpf(x) otherwise where lpf(x) is the least prime factor of x. a(n) = -1 if 1 is never reached.

0, 1, 4, 2, 8, 5, 9, 3, 6, 9, 11, 6, 12, 10, 7, 4, 12, 7, 14, 10, 8, 12, 14, 7, 11, 13, 8, 11, 15, 8, 14, 5, 9, 13, 9, 8, 16, 15, 9, 11, 16, 9, 17, 13, 10, 15, 17, 8, 10, 12, 9, 14, 18, 9, 13, 12, 10, 16, 17, 9, 19, 15, 10, 6, 10, 10, 20, 14, 11, 10, 18, 9, 20

Offset: 1

Author

Ya-Ping Lu, Jun 23 2025

Keywords

• nonn

Comments

First 8 terms are the same as those in A339991.

Conjecture: a(n) != -1.

Links

• Ya-Ping Lu, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A339991.

Programs

Python

from sympy import isprime, primefactors
def A384713(n, c = 0):
    while n != 1: n = n//2 if n%2 == 0 else n*n-1 if isprime(n) else n-min(primefactors(n)); c += 1
    return c