Partial-Sum -> Some Primes

[Jim Nastos]

On Fri, 13 Feb 2004, Leroy Quet wrote:

> Let a(1) = 1;
> Let a(m) be the lowest yet unpicked positive integer such that:
> sum{k=1 to m} k* a(k)
> is a prime.
> Figured by hand, so very well could be wrong, I get:
> 
> a(k) : 1, 2, 4, 3, 6, 5, 12, 7,...
> 
> Question:
> Is this a permutation of the positive integers?
> If so, its inverse-permutation is:
> 1, 2, 4, 3, 6, 5, 8,...
> (I get some EIS matches for the few terms I give for the inverse 
> permutation, but no matches for the primary sequence.)

  Somewhat interesting... what is the sequence of primes
obtained from these k*a(k) series?

J