OT: squarefree sequence
- Just a bit off-topic, but combining the squarefree concept with
sequences of the form k*2^n+1, I found this factoid:
70785*2^n+1 is squarefree for 0 <= n <= 153.
Note that any k with such a long sequence of squarefree numbers
is also probably a good k for yielding primes; in order to be
squarefree for such a long run, the members of the sequence must
be free of small divisors.
[Note: I tried to come back to the topic of prime numbers :) ]
On the other side of the coin:
27887*2^n+1 is non-squarefree for 0 <= n <= 4.
Similarly, such values of k are probably not good k values for