[Fwd: Reply from On-Line Encyclopedia of Integer Sequences (fwd)]

[David W. Wilson]

I forgot to copy this to seqfan.

"David W. Wilson" wrote:
> 
> Richard Guy wrote:
> >
> > This is the sequence of `Pillai primes' (so named in
> > a preprint of G E Hardy \& M V Subbarao, A modified
> > problem of Pillai and some related questions.
> >
> > A Pillai prime $p$ is one such that there exists an
> > integer $n$ such that $n!+1 \equiv 0 \bmod p$ and
> > $p \not\equiv 1 \bmod n$.
> >
> > They also define `those natural numbers $m$ with the
> > property that for each $m$ there is a corresponding
> > prime $p$ satisfying $m!+1 \equiv 0 \bmod p$ and
> > $p \not\equiv 1 \bmod m$.
> >
> > These are  8 9 13 14 15 16 17 18 19 22 ...
> 
> The only reasonable approach I can see to extending this sequence involves
> factoring m!+1 to get p, and I am not in possession of heavy-duty factoring
> software.  Already 22!+1 blows my 64-bit integer capacity.
> 
> > ---------- Forwarded message ----------
> > Date: Fri, 14 Sep 2001 11:34:48 -0400 (EDT)
> > From: sequences-reply at research.att.com
> > To: rkg at cpsc.ucalgary.ca
> > Subject: Reply from On-Line Encyclopedia of Integer Sequences
> >
> > Matches (up to a limit of 50) found for  23 29 59 61 67 71 79 83 100 137:
> 
> As I was not following this thread very closely, forgive me if I am not
> the first to observe that 100 above should be 109.
> 
> I compute the Pillai primes:
> 
> 23 29 59 61 67 71 79 83 109 137 139 149 193 227 233 239 251 257 269 271
> 277 293 307 311 317 359 379 383 389 397 401 419 431 449 461 463 467 479
> 499 503 521 557 563 569 571 577 593 599 601 607 613 619 631 641 647 661
> 
> > [failed sequence lookup output omitted]
> 
> I was unable to find "23 29 59 61 67 71", so I assume the Pillai primes
> are not in the EIS.