prime chains generated by f(x)=ax+b

[Don McDonald]

In message
<Pine.GSO.4.21.0306120854250.25408-100000 at tarski.math.usf.edu>
Edwin wrote:
> 
> Don,
> 
> I just saw your message. This is just to let you know that I am
> (slowly) working on prime chains of the type p, f(p), f(f(p)),...
> for f(x)=ax+b for small values of a and b. This is not original with me,
> of course. Apparently this is discussed in the paper by Lehmer:
...
Thanks Edwin.. appreciated.

>
> Last night I ran a program to find the sequences a(n) = p where p is the
> first prime such that for i from 0 to n-1  (f@@i)(p) is prime. (Here
> (f@@i) is the Maple code for f composed with itself i times.) I did it for
> the functions below. Each was run for just 15 minutes using Maple and a
> not very efficient program:
...
Interesting results.

f(t) = 2*t+1, [2, 2, 2, 2, 2, 89, 1122659, 19099919]

I am familiar with the Cunningham chain, Sophie Germaine Primes,
2 5 11 23 47.
i.e. (f@@4)(2)  ??

I do not have Maple, Mathematica or Tex. I do however have a Pari.

...
> f(t) = 3*t+2, [2, 3, 5, 29, 1129, 10009, 575119]

As posted by Edwin Clark and subsequently
oeis SEQ A083388,  by don.mcdonald.
[which needs editing.]

(PARI program for Acorn Archimedes RISC OS,
reduced instruction set computer.)

> Some of these are known and/or easily explainable, like, t+2, t+4, t+6,
> 2t+1, 2t-1. I may understand the other short sequences better
> after I read the above mentioned papers --which I haven't done yet.
> I plan to enter the ones not already in the OEIS in a day or so.
>
I do not have a library or university. (I am a poor reader
and struggling writer.)

SEQ A081173. f(x) = x^x+2.  by don.mcdonald.

> --Edwin
>
> PS I found your message a little hard to decipher. Could you state more
> succintly the relationship to the above if any. Thanks.

I will do my best, please.

-- Don.
13.06.03  23:17.