OFFSET
3,1
COMMENTS
Each term is only conjectured and has been verified up to 10^6.
Note a(2) is undefined if there are infinitely many Mersenne primes.
EXAMPLE
For example, a(3) = 16 because 16 * 17 * 18 = 2^5 * 3^2 * 17 admits only three prime divisors (2, 3, and 17) and appears to be the largest product of three consecutive integers with the property.
PROG
(SageMath)
for r in range(3, 100):
history = []
M = 0
for n in range(1, 100000):
primes = {p for p, _ in factor(n)}
history.append(primes)
history = history[-r:]
total = set()
for s in history: total |= s
# Skip if too many primes.
if len(total) > r: continue
if n > M: M = n
print(r, M-r+1)
CROSSREFS
KEYWORD
nonn
AUTHOR
Onno M. Cain, Sep 06 2019
STATUS
approved