Second sequence

Whilst still in my prime,
It seemed a good time
That I ask you all think
what is the integral link?

Before you all curse
This one's like my first
Though the pattern in this sequel
is not the first's equal

3/2 it did start
and the next? 1 apart!
98,218, these both over three
144244/5 is another we see

Before giving the quest,
Leaving some of you hexed...
The latest was 866 over three
Your turn now, the next one will be?...

3/2, 5/2, 98/3, 218/3, 144244/5, 866/3, ?

Apologies for the dodgy poem but there is a hint or two in there :]

No time to solve this, but compliments for the cute poem 🙂

Heh...cheers, though in retrospect I think I'm asking a bit too much in this particular problem, and the first number in the sequence can be argued that it doesn't belong with the standard definition of prime numbers (ie: 1 isn't a prime)

There is a skill to setting a good puzzle that I have yet to acquire!

Originally posted by Agerg
Heh...cheers, though in retrospect I think I'm asking a bit too much in this particular problem, and the first number in the sequence can be argued that it doesn't belong with the standard definition of prime numbers (ie: 1 isn't a prime)

There is a skill to setting a good puzzle that I have yet to acquire!

No no, I think you have a good point.
I have long argued that 1 should be considered prime, since the definition of a prime is that it "can only be divided by itself and 1" just because itself IS 1 shouldn't preclude it from being considered prime--- says I!

Originally posted by telecomladyj
No no, I think you have a good point.
I have long argued that 1 should be considered prime, since the definition of a prime is that it "can only be divided by itself and 1" just because itself IS 1 shouldn't preclude it from being considered prime--- says I!

If we let 1 be prime we lose the unique factorisation of the integers (up to ordering that is). No longer can we say 12 = 2 x 2 x 3, since we can also factorise it as
1 x 1 x 1 x 2 x 2 x 3 or
1 x 2 x 2 x 3 or
.
.
.
1 x 1 x 1 x 1 x 1 x 1 x 1 x 1 x 1 x 1 x 2 x 2 x 3
😵

Originally posted by telecomladyj
No no, I think you have a good point.
I have long argued that 1 should be considered prime, since the definition of a prime is that it "can only be divided by itself and 1" just because itself IS 1 shouldn't preclude it from being considered prime--- says I!

A non-prime is a number composed of two or more primes. Like 6=3x2. Right?
So if 1 is a prime, then 5 is a non-prime, because 5=5x1.

By including 1 in the set of primes, then you have to exclude 1 every time you want to have a unique factorization. Very impractical.

No 1 is not a prime for practical reasons.