cp's OEIS Frontend

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.

%I A384713 #15 Jul 04 2025 01:11:21
%S A384713 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,
%T A384713 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,
%U A384713 13,12,10,16,17,9,19,15,10,6,10,10,20,14,11,10,18,9,20
%N 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.
%C A384713 First 8 terms are the same as those in A339991.
%C A384713 Conjecture: a(n) != -1.
%H A384713 Ya-Ping Lu, <a href="/A384713/b384713.txt">Table of n, a(n) for n = 1..10000</a>
%o A384713 (Python)
%o A384713 from sympy import isprime, primefactors
%o A384713 def A384713(n, c = 0):
%o A384713     while n != 1: n = n//2 if n%2 == 0 else n*n-1 if isprime(n) else n-min(primefactors(n)); c += 1
%o A384713     return c
%Y A384713 Cf. A339991.
%K A384713 nonn
%O A384713 1,3
%A A384713 _Ya-Ping Lu_, Jun 23 2025