A071810

[franktaw at netscape.net]

This sequence (Number of subsets of the first n primes whose sum is a 
prime) has the comment "... a(n+1) < 2*a(n). Therefore Lim -> oo, 
a(n)/2^n = 0".  I have two problems with this:

1) It is not obvious that a(n+1) < 2*a(n).
2) The "therefore" does not follow.

So,

1) Can anybody show that a(n+1) < 2*a(n) [for n > 1].
2) Can anybody show that a(n+1) < c*a(n) for some c < 2 and n 
sufficiently large?
3) Note that (2) suffices to prove the limit above.  Failing that, some 
other proof of the limit would be nice.
4) Can anybody evaluate lim_{n->infinity} a(n+1)/a(n)?

Franklin T. Adams-Watters

________________________________________________________________________
Check Out the new free AIM(R) Mail -- 2 GB of storage and 
industry-leading spam and email virus protection.