weighted voting sequences

[Joerg Arndt]

so that when you come across a sequence in your work, 
sequence - that would take more time than I have available.
send me more precise definitions.
Return-Path: <jvospost3 at gmail.com>
X-Ids: 165
DKIM-Signature: a=rsa-sha1; c=relaxed/relaxed;
        d=gmail.com; s=beta;
        h=domainkey-signature:received:received:message-id:date:from:to:subject:cc:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references;
        b=rtbvWqQNL0y7upsL3gKBcNxhUDGa0Lj+cR+bNeMa8uWvu+bUk1P6xAwv7NWzPfUgqLUh7vortlAQh4yY3/kk9T64EjwhZFlA4I/dEjYxYRaxN1iz714wIa1lgwnw6JYDDwevoMDMzx5q/nOCtgwVzJMazJh/PngHfku0d4Lte58=
DomainKey-Signature: a=rsa-sha1; c=nofws;
        d=gmail.com; s=beta;
        h=received:message-id:date:from:to:subject:cc:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references;
        b=DMQOxaWf8bqYEWoE14TvyaJZe9rOb4s9ObMoAvNuV/witTIBZUtBZFMHYEpxjB+e7MfxoofytCHs8K8egX6FFqeiVNTPLIOEdThyCFWhdk5MHrNULTwl8RRNBihnCWDxOZb0JBYzoR/S4qN4nf57zGK0iWm36mAbEtKeAQdZ5/g=
Message-ID: <5542af940707281505n357500fbu2fada9399c6b518c at mail.gmail.com>
Date: Sat, 28 Jul 2007 15:05:59 -0700
From: "Jonathan Post" <jvospost3 at gmail.com>
To: "Max Alekseyev" <maxale at gmail.com>
Subject: Re: definition of anti-divisor
Cc: "Maximilian Hasler" <maximilian.hasler at gmail.com>,
   "Sequence Fans" <seqfan at ext.jussieu.fr>, jvospost2 at yahoo.com
In-Reply-To: <5542af940707242126q68201c55pf5c674ce6848194f at mail.gmail.com>
MIME-Version: 1.0
Content-Type: text/plain; charset=ISO-8859-1
Content-Transfer-Encoding: 7bit
Content-Disposition: inline
References: <200707211141.l6LBf9dn795643 at fry.research.att.com>
	 <5542af940707212354t4b733f7cof101bc0b7960d64b at mail.gmail.com>
	 <5542af940707221117t4e411e40o840c9228f2e9b7f8 at mail.gmail.com>
	 <3c3af2330707231221y5690ec3cm473f38b5f2bc6adc at mail.gmail.com>
	 <5542af940707231709n330ca0ffkc581bb34984b1154 at mail.gmail.com>
	 <5542af940707231811t4044fa14rcdc33c9a227a9562 at mail.gmail.com>
	 <d3dac270707231857y6dae1f1cq27367b56568301cb at mail.gmail.com>
	 <d3dac270707231929r558496f6t36dfb40745bb02fe at mail.gmail.com>
	 <d3dac270707232202q7d6d4198t259627c7b9977368 at mail.gmail.com>
	 <5542af940707242126q68201c55pf5c674ce6848194f at mail.gmail.com>
X-Greylist: IP, sender and recipient auto-whitelisted, not delayed by milter-greylist-3.0 (shiva.jussieu.fr [134.157.0.165]); Sun, 29 Jul 2007 00:06:02 +0200 (CEST)
X-Virus-Scanned: ClamAV 0.88.7/3797/Sat Jul 28 21:36:26 2007 on shiva.jussieu.fr
X-Virus-Status: Clean
X-j-chkmail-Score: MSGID : 46ABBDC9.002 on shiva.jussieu.fr : j-chkmail score : X : 0/50 1 0.569 -> 1
X-Miltered: at shiva.jussieu.fr with ID 46ABBDC9.002 by Joe's j-chkmail (http://j-chkmail.ensmp.fr)!

NEW SEQUENCE FROM Jonathan Vos Post

%I A000001
%S A000001 3, 18, 1728, 679477248
%N A000001 Anti-primorials, partial products of anti-primes A092680.
%C A000001 This is to primorial (A002110) as anti-prime (A092680) is
to prime (A000040). Max Alekseyev <maxale at gmail.com> points out
 that every element of A066466, except 4, must be of the form 3*2^k
such that 3*2^(k+1)-1, 3*2^(k+1)+1 are twin primes. There no such new
k+1 (i.e., except known 1,2,6,18) below 1000.
In other words, 3*2^n - 1, 3*2^n + 1 are twin primes for n=1,2,6,18.
 According to these tables:
http://www.prothsearch.net/riesel.html
http://www.prothsearch.net/riesel2.html
there are no other such n up to 1200000.
Therefore, the next element of A066466 (if it exists) is greater than
3*2^1200000 ~= 10^361236. Hence the next element of the
anti-primorials (if it exists) is greater than 679477248 *3*2^1200000
~= 679477248 *
 10^361236 ~= 6 * 10^361245.
%D A000001 1.
%F A000001 a(n) = PRODUCT[k = 1..n] A092680(k).
%e A000001 a(1) = 3.
a(2) = 3 * 6 = 18.
a(3) = 3 * 6 * 96 = 1728.
a(4) = 3 * 6 * 96 * 393216 = 679477248.
%Y A000001 Cf. A000040, A002110, A092680, A130874.
%O A000001 1,1
%K A000001 ,nonn,unkn,
%A A000001 Jonathan Vos Post (jvospost2 at yahoo.com), Jul 28 2007
RH
RA 192.20.225.32