OFFSET
1,2
COMMENTS
After 5 million terms the lowest number not to have appeared is 16 = 2^4. In that range 2 is a factor of 2614180 terms while 3 is a factor of 1763610 terms. As these are the most and second-most common prime factors this suggest that 16, and other higher powers of 2, will never appear as that would require 2 to be the least common factor of all previous terms. This is also true for the powers of the other smaller primes.
In the first 5 million terms the only fixed point, other than the first two terms, is 4175, although it is probable that more exist.
LINKS
Scott R. Shannon, Table of n, a(n) for n = 1..10000
Scott R. Shannon, Image of the first 100000 terms. The green line is a(n) = n.
Scott R. Shannon, Image of the first 5000000 terms
EXAMPLE
a(5) = 3 as the list of primes that divide all previous terms a(1)..a(4) is 2 and 3, with 2 being a factor of three terms and 3 being a factor of one term. Therefore a(5) is the lowest multiple of 3 that has not appeared, which is 3.
CROSSREFS
KEYWORD
nonn,look
AUTHOR
Scott R. Shannon, Apr 03 2023
STATUS
approved