A Strange Sequence not in the OEoIS

[Joerg Arndt]

btw these guys are useful for computing logarithms:

factor x^2-1 for x in

51744295
170918749
265326335
287080366
362074049
587270881
617831551
740512499
831409151
1752438401
2151548801
2470954914
3222617399

then see http://www.jjj.de/fxt/#fxtbook
p.628, sect.31.4, "Simultaneous computation of logarithms of small primes"

One can search for numbers x such that P(x) (P a polynomial)
is B-smooth (for moderate B) extremely fast (e.g. P=x^2+-1
and using the first 64 primes: 500 Million tests per second).

However, determining the _largest_ number x such that is, say,
B-smooth with P(x):=x^2+-1 is not possible:
I'd like to see a proof that the set is even _finite_!

cheers,   jj


* Jack Brennen <jb at brennen.net> [Mar 25. 2008 08:36]:
> David Harden wrote:
>> I think, though I haven't checked, that the fourth and fifth terms are, 
>> respectively,
> > 4801^2 - 1 = 23049600 and 19601^2 - 1 = 384199200.
>
> 8749^2 - 1 = 76545000 = 2^3 * 3^7 * 5^4 * 7.
>
>
> An alternative way to express the sequence, at least how I thought of
> it:  largest A such that A-1 and A+1 are both p-smooth, where p is the
> nth prime.  Your sequence gives the (A-1)*(A+1) products.
>