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<DIV>Here's one:</DIV>
<DIV> A005843 even numbers</DIV>
<DIV> A008585 multiples of 3</DIV>
<DIV> A008593 multiples of 11</DIV>
<DIV> A042948 congruent to 1,2 mod 4</DIV>
<DIV> A047476 congruent to 0,1,2,3 mod 8</DIV>
<DIV> </DIV>
<DIV>Any number of others could be added to this list, such as A001597, perfect powers; or A002113, palindromes.</DIV>
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<DIV>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.)</DIV>
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<DIV>Franklin T. Adams-Watters<BR> <BR>-----Original Message-----<BR>From: Ed Pegg Jr <A href="mailto:edp@wolfram.com">edp@wolfram.com</A><BR><BR>
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<DIV class=AOLPlainTextBody id=AOLMsgPart_0_ced9b0cb-35bb-48de-b43b-7616109843de>Primes and Fibonacci numbers are Venn-2. That is, there are numbers which are (!=not) <BR>P&F, !P&F, P&!F, !P&!F <BR> <BR>All 2^2 possibilities are represented. <BR> <BR>Is there a set of Venn-5 sequences, such that numbers exist for <BR>all 2^5 combinations? <BR> <BR>Ed Pegg Jr <BR> <BR></DIV><!-- end of AOLMsgPart_0_ced9b0cb-35bb-48de-b43b-7616109843de --></DIV></DIV>
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