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.

2, 3, 13, 5, 13, 7, 17, 13, 37, 11, 41, 13, 29, 41, 61, 17, 37, 19, 41, 37, 613, 23, 613, 41, 53, 613, 109, 29, 61, 31, 829, 61, 1861, 61, 73, 37, 277, 73, 157, 41, 613, 43, 89, 613, 181, 47, 97, 613, 101, 97, 401, 53, 109, 101, 113, 109, 229, 59, 829, 61, 241

Offset: 2

Author

Ya-Ping Lu, Jun 09 2025

Keywords

• nonn

Comments

Conjecture: a(n) != -1.

Examples

			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.
		

Crossrefs

Cf. A020639 (lpf), A383777.

Programs

Python

from sympy import isprime, primefactors
for n in range (2, 63):
    while not isprime(n): n = n - min(primefactors(n)) if n%2 else 2*n + 1
    print(n, end = ', ')

Formula

a(n) = n if n is a prime; > n otherwise.

a(n) mod 4 = 1 unless n is a prime and n mod 4 = 3.