sequences containing no prime

franktaw at netscape.net franktaw at netscape.net
Sat Oct 22 05:00:21 CEST 2005


 The next terms are 132,141,143,144,145,152,156,173,252 (if I did not make a mistake).
There are no others up to 287; I was unable to determine whether A000287 contains any primes,
partly because its definition is unclear.
 
Incidently, several of these early sequences should have the "more" keyword.
A000173 - in the list above - is the one I noted, but there were others.
 
Franklin T. Adams-Watters
16 W. Michigan Ave.
Palatine, IL 60067
847-776-7645
 
 
-----Original Message-----
From: N. J. A. Sloane <njas at research.att.com>
To: seqfan at ext.jussieu.fr
Sent: Fri, 21 Oct 2005 22:09:20 -0400 (EDT)
Subject: Re sequences containing no prime



Thanks Alonso for this suggestion.  I checked up through A000128.
Most of them do contain a prime.  If I did not make a mistake,
the sequence (which will be in the OEIS in a moment) begins
as follows:

%I A111157
%S A111157 4,7,12,35,56,66,82,118
%N A111157 Numbers n such that sequence A_n in this database does not contain a 
prime.
%C A111157 That is, the complete sequence A_n, not just the terms that are shown 
in the entry, does not contain a prime or the negative of a prime. The only 
exception to this is for sequences with keyword "dead", when only the visible 
terms are to be considered.
%C A111157 No other terms below 128.
%O A111157 1,1
%K A111157 nonn,dumb,more
%H A111157 PrimeFan, <a href="http://www.geocities.com/primefan/EsotericIntegerSequences.html">Esoteric 
Integer Sequences</a> (Gives a different version.)
%A A111157 njas, following a suggestion of Alonso Del Arte (alonso.delarte(AT)gmail.com), 
Oct 21 2005
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