OFFSET
0,2
COMMENTS
In fact a(n) = A374983(n) + 1 (see the proof in A374983), but this was unproved when this sequence was created, and in any case the prime factors of A374983(n) and a(n) are both of interest, so both sequences are included in the OEIS. Both sequences grow doubly exponentially. See also A375791.
One might be led to conjecture that the last 4 digits of the numbers from a(5) onwards are always 1200, but Rémy Sigrist has observed that this does not hold for a(10) = 23554197523775043569951631809272942045755944094320810352530343995293765200.
LINKS
N. J. A. Sloane, Table of n, a(n) for n = 0..14
Rémy Sigrist, Proof of theorem about A374983 and the present sequence, Aug 26 2024, revised Sep 01 2024.
PROG
(Python)
from itertools import count, islice
from math import gcd
def A375516_gen(): # generator of terms
p, q = 0, 1
for k in count(1):
yield q
m = q//(k*(q-p))+1
p, q = p*k*m+q, k*m*q
p //= (r:=gcd(p, q))
q //= r
CROSSREFS
KEYWORD
nonn,frac
AUTHOR
N. J. A. Sloane, Aug 19 2024
STATUS
approved