A384874 a(n) is the first prime encountered when iterating the map x -> x/2 if x is even, x*lpf(x) + 1 otherwise, where lpf(x) is the least prime factor of x, on n >= 2; or -1 if a prime is never reached.

2, 3, 2, 5, 3, 7, 2, 7, 5, 11, 3, 13, 7, 23, 2, 17, 7, 19, 5, 2, 11, 23, 3, 313, 13, 41, 7, 29, 23, 31, 2, 313, 17, 11, 7, 37, 19, 59, 5, 41, 2, 43, 11, 17, 23, 47, 3, 43, 313, 5869, 13, 53, 41, 13, 7, 43, 29, 59, 23, 61, 31, 313, 2, 163, 313, 67, 17, 13, 11

Offset: 2

Author

Ya-Ping Lu, Jun 11 2025

Keywords

• nonn

Comments

Conjecture: a(n) != -1.

For n <= 24, this sequence is the same as A320028.

Links

• Ya-Ping Lu, Table of n, a(n) for n = 2..1000
• Ya-Ping Lu, A plot of a(n) for n <= 1000

Crossrefs

Cf. A006370, A320028, A384698.

Programs

Python

from sympy import isprime, primefactors
def A384874(n):
    while not isprime(n): n = n*min(primefactors(n))+1 if n%2 else n//2
    return n