Venn 5 sequence set

[franktaw at netscape.net]

Here's one:
 A005843 even numbers
 A008585 multiples of 3
 A008593 multiples of 11
 A042948 congruent to 1,2 mod 4
 A047476 congruent to 0,1,2,3 mod 8
 
Any number of others could be added to this list, such as A001597, perfect powers; or A002113, palindromes.
 
If we don't require the sequences to be in the OEIS, multiples of p for each prime p is an infinite set, such that each finite subset has all 2^n combinations present.  (It is of course not possible for every combination of an infinite set of sequences to be present, because the number of such combinations is uncountable.  There are non-standard models of the integers where every combination of this example is represented.)
 
Franklin T. Adams-Watters
 
-----Original Message-----
From: Ed Pegg Jr edp at wolfram.com


Primes and Fibonacci numbers are Venn-2. That is, there are numbers which are (!=not) 
P&F, !P&F, P&!F, !P&!F 
 
All 2^2 possibilities are represented. 
 
Is there a set of Venn-5 sequences, such that numbers exist for 
all 2^5 combinations? 
 
Ed Pegg Jr 
 
___________________________________________________
Try the New Netscape Mail Today!
Virtually Spam-Free | More Storage | Import Your Contact List
http://mail.netscape.com
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://list.seqfan.eu/pipermail/seqfan/attachments/20060419/99f10dd7/attachment-0001.htm>