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<DIV>floor(cos(0)) = 1, which does not occur in floor(sin(n)); but other than that, all finite substrings in either occur in the other. Both sequences are of the form floor(sin(n+K)), and the only case where (n+K)/(2Pi) is an integer is for n=0. So leaving aside n=0, the value of floor(sin(x)) in some neighborhood of n+K is constant. These intervals can be translated back to the starting point of the sequence, and intersected to give a single interval. Since multiples of 1 mod 2Pi are dense, we can find n'+K' which is in that interval, providing the starting point for the matching sequence. For the case n=0 with the sin function, we are restricted to a half-open interval starting at zero, but otherwise the same argument works. (And, as indicated, n=0 for the cosine does not work.)</DIV>
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<DIV>The same kind of argument will establish that the sequences for rounded sin and cos contain all of each other's finite subsequences.</DIV>
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<DIV>Franklin T. Adams-Watters<BR>16 W. Michigan Ave.<BR>Palatine, IL 60067<BR>847-776-7645</DIV>
<DIV> </DIV> <BR>-----Original Message-----<BR>From: Tautócrona <tautocrona@terra.es><BR>To: seqfan@ext.jussieu.fr<BR>Sent: Mon, 7 Nov 2005 00:09:00 +0100<BR>Subject: Related sequences not related in database + question<BR><BR>
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By the way, are all substrings of {floor(sin(n))} contained in {floor(cos(n))}
and
conversely ? Any results about this type of statements?
Regards. Jose Brox
<A href="http://espanol.groups.yahoo.com/group/Telecomunicacion/" target=_blank>http://espanol.groups.yahoo.com/group/Telecomunicacion/</A>
<A href="mailto:ambroxius%40terra.es">ambroxius@terra.es</A>
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