# Reply from On-Line Encyclopedia of Integer Sequences (fwd)

Richard Guy rkg at cpsc.ucalgary.ca
Fri Sep 14 21:50:30 CEST 2001

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 ...

---------- Forwarded message ----------
Date: Fri, 14 Sep 2001 11:34:48 -0400 (EDT)
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  :

Even though there are a large number of sequences in the table, at least
one of yours is not there! Please send it to me using
the submission form on the sequence web page
http://www.research.att.com/~njas/sequences/Submit.html
and I will (probably) add it!  Include a brief description. Thanks!

o  Take a look at my web page which does lookups "online"!  Go to:
http://www.research.att.com/~njas/sequences/
o  The whole sequence table is also visible there, as well as
an explanation of the symbols used in the table.
o  If your sequence was not in the table,
please send it to me using the submission form on the web page!
o  There is a second sequence server (superseeker at research.att.com)
that tries hard to find an explanation.  Only 1 request per person