A073608

[Don Reble]

Jim, et al.

> ID Number: A073608
> Sequence:  1,3,5,8,10
> Name:      a(1) = 1, a(n) = smallest number such that a(n)-a(n-k) is a 
>            prime or a prime power for all k.
> Comments:  Differences |a(i)-a(j)| are primes or prime powers for all i,j.
> Conjecture: sequence is bounded.

    I believe the author intended to exclude "1" from the set of prime
    powers. (Even though it is the zeroth power of my favorite prime.)

> For the proof of this, I require the sixth term, 
> Assume some k was the 7th term...
...
> which is impossible.
> Is there a more fundamental proof that doesn't use the
> knowledge of the 6th term? If there didn't exist a 6th term (or if it was 
> extremely difficult to find) would there still be an elementary proof?

    There is an elementary proof that no set of seven integers of that
    kind exists.
--
Don Reble       djr at nk.ca