OFFSET
1,2
COMMENTS
Only the composites are replaced by a prime; 1 and the primes themselves stay as they are. A composite "c" is replaced by the concatenation [az], where "a" is the smallest factor > 1 of "c" and "z" the biggest factor < "c". This transforms for instance 28 in [214] (because 2 x 14 is 28) and not in [128] (1 x 28) or [47] (4 x 7). The procedure is iterated from there until the concatenation produces a prime [214 becomes 2107, then 7301, 71043, 323681, 431751, 3143917, 7449131, 12895779, 34298593, 74899799, 135761523, 345253841, 941366901 which ends into the prime 3313788967, prime that will thus be a(28)].
LINKS
Jean-Marc Falcoz, Table of n, a(n) for n = 1..175
EXAMPLE
As the first three natural numbers (1, 2 and 3) are not composites, they stay as they are. Then 4 becomes 22, and 22 produces the prime 211; 5 is a prime; 6 becomes the prime 23; 7 is a prime; 8 ends on the prime 2692213; 9 becomes 33 and 33 produces the prime 311; 10 produces the chain 25, 55, 511, 773 (prime); etc.
Some terms of this sequence are huge: a(158) is a 70-digit prime, for instance.
PROG
(Python)
from sympy import factorint
def A316941(n):
while n>1 and sum((f:=factorint(n)).values()) > 1:
n = int(str(p:=min(f))+str(n//p))
return n # Chai Wah Wu, Aug 02 2024
CROSSREFS
KEYWORD
base,nonn
AUTHOR
Eric Angelini and Jean-Marc Falcoz, Jul 17 2018
STATUS
approved