See also https://en.wikipedia.org/wiki/Cunningham_chain On Thu, Dec 26, 2019 at 12:22 PM Henry Baker <hbaker1@pipeline.com> wrote:

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 ?

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