OFFSET
1,2
COMMENTS
For any prime number p, the sequence contains a multiple of p, say a(k), and this term satisfies a(k-1)*a(k) = p!.
LINKS
Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, PARI program
EXAMPLE
The first terms are:
n a(n) a(n)*a(n+1)
-- ------- -----------
1 1 2!
2 2 3!
3 3 4!
4 8 5!
5 15 6!
6 48 7!
7 105 8!
8 384 9!
9 945 10!
10 3840 11!
11 10395 12!
12 46080 13!
13 135135 14!
14 645120 15!
15 2027025 13!
16 3072 12!
PROG
(Python)
from itertools import count, islice
def agen(): # generator of terms
fset, aset, an = set(), set(), 1
while True:
yield an
aset.add(an)
fk = 1
for k in count(2):
fk *= k
q, r = divmod(fk, an)
if r == 0 and q not in aset:
an = q
break
print(list(islice(agen(), 48))) # Michael S. Branicky, Mar 14 2025
(PARI) \\ See Links section.
CROSSREFS
KEYWORD
nonn
AUTHOR
Rémy Sigrist, Mar 14 2025
STATUS
approved
