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

1,3

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

Prog

(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

Crossrefs

Cf. A339991.

Sequence in context: A030210 A367110 A339991 * A098798 A392859 A131783

Adjacent sequences: A384710 A384711 A384712 * A384714 A384715 A384716

Keyword

nonn

Author

Ya-Ping Lu, Jun 23 2025

Status

approved