A073608

[Jim Nastos]

On Sat, 10 Aug 2002, Don Reble wrote:

> > 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.)

  Nowhere is there an implication that 1 is a prime power. If the author 
assumed that, then the sequence would be 1,2,3,4,5,6. 

>     There is an elementary proof that no set of seven integers of that
>     kind exists.

  Okay. Any elaboration or reference on that?

Jim