cp's OEIS Frontend

A384698 The first prime number reached by iterating the map, x -> 2*x + 1 if x is even; x - lpf(x) otherwise where lpf(x) is the least prime factor of x, on n >= 2; or -1 if a prime is never reached.

%I A384698 #23 Jun 15 2025 19:52:28
%S A384698 2,3,13,5,13,7,17,13,37,11,41,13,29,41,61,17,37,19,41,37,613,23,613,
%T A384698 41,53,613,109,29,61,31,829,61,1861,61,73,37,277,73,157,41,613,43,89,
%U A384698 613,181,47,97,613,101,97,401,53,109,101,113,109,229,59,829,61,241
%N A384698 The first prime number reached by iterating the map, x -> 2*x + 1 if x is even; x - lpf(x) otherwise where lpf(x) is the least prime factor of x, on n >= 2; or -1 if a prime is never reached.
%C A384698 Conjecture: a(n) != -1.
%F A384698 a(n) = n if n is a prime; > n otherwise.
%F A384698 a(n) mod 4 = 1 unless n is a prime and n mod 4 = 3.
%e A384698 a(4) = 13 because iterating the map on n = 4 reaches a prime, 13, in three steps: 4 -> 2*4+1=9 -> 9-3=6 -> 2*6+1=13.
%o A384698 (Python)
%o A384698 from sympy import isprime, primefactors
%o A384698 for n in range (2, 63):
%o A384698     while not isprime(n): n = n - min(primefactors(n)) if n%2 else 2*n + 1
%o A384698     print(n, end = ', ')
%Y A384698 Cf. A020639 (lpf), A383777.
%K A384698 nonn
%O A384698 2,1
%A A384698 _Ya-Ping Lu_, Jun 09 2025