Bingo! Thanks! So my F(p) is actually "Sophie Germain degree" of p. It appears that my F(p)>6 may be exceedingly rare. I wonder how fast F^(-1) grows... At 08:40 AM 12/26/2019, Fred Lunnon wrote:
See OEIS A063377 : Sophie Germain sequence, tabulated up to p = 10^5 by Antti Karttunen (though omitting p = 0 !)
WFL
On 12/26/19, Henry Baker <hbaker1@pipeline.com> wrote:
Consider the sequence of integers generated by:
Given a prime p,
Ap_0 = p Ap_(n+1) = 2*Ap_n + 1
This sequence *terminates* when Ap_n *isn't* prime.
Finally, define the function F(p), p prime, as the *length* of this sequence Ap_n.
Informally, F(p) is the length of an all-prime sequence consisting of p, 2p+1, 2(2p+1)+1, ...
These sequences of primes seem to be common enough, that I'm guessing that for *every* n, there exists a prime p such that F(p)=n.
Here's the real kicker: there probably isn't a prime p s.t. F(p)=oo, is there ?