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<TITLE>Re: First, second, third... differences (corrected)</TITLE>
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<DIV id=idOWAReplyText3050 dir=ltr>
<DIV dir=ltr><FONT color=#000000 size=2>Eric (me) wrote:</FONT></DIV>
<DIV dir=ltr><FONT size=2>> 1 1 1 1 2 2 2 2 4 4 4 4 8 8 8 8 16 16 16 16 32 32
32 32 64 64 64 64 ...</FONT>
<DIV dir=ltr><FONT size=2>> I'm looking for less trivial
ones...</FONT></DIV></DIV></DIV>
<DIV dir=ltr><FONT size=2></FONT> </DIV>
<DIV dir=ltr><FONT size=2>I've just found this seq. (among others) which is
equal to it's fourth</FONT></DIV>
<DIV dir=ltr><FONT size=2>absolute diff.:</FONT></DIV>
<DIV dir=ltr><FONT size=2></FONT> </DIV>
<DIV dir=ltr><FONT size=2>7 1 5 3 14 2 10 6 28 4 20 12 56 8 40 24 112 16 80 48
224 32 160 96 448 ..</FONT></DIV>
<DIV dir=ltr><FONT size=2></FONT> </DIV>
<DIV dir=ltr><FONT size=2>The similar seq. below (first terms in different
order) enters in another</FONT></DIV>
<DIV dir=ltr><FONT size=2>4th-absolute-diff sequence:</FONT></DIV>
<DIV dir=ltr><FONT size=2></FONT> </DIV>
<DIV dir=ltr><FONT size=2>1 3 5 7 2 6 10 14 4 12 20 28 8 24 40 56 16 48 80 112
32 96 160 224 64 ...</FONT></DIV>
<DIV dir=ltr><FONT size=2>enters in:</FONT></DIV>
<DIV dir=ltr><FONT size=2>3 1 1 1 6 2 2 2 12 4 4 4 24 8 8 8 48 16 16 16 96 32 32
32 192 64 64 64 ...</FONT></DIV>
<DIV dir=ltr><FONT size=2>which loops.</FONT></DIV>
<DIV dir=ltr><FONT size=2></FONT> </DIV>
<DIV dir=ltr><FONT size=2>Best,</FONT></DIV>
<DIV dir=ltr><FONT size=2>E.</FONT></DIV>
<DIV dir=ltr><BR><FONT size=2>
<HR tabIndex=-1>
<B>De:</B> Eric Angelini<BR><B>Date:</B> dim. 07/01/2007 23:16<BR><B>À:</B>
seqfan@ext.jussieu.fr<BR><B>Cc:</B> alexandre.wajnberg@skynet.be<BR><B>Objet
:</B> Second _absolute_ differences<BR><BR></FONT></DIV>
<DIV>
<DIV id=idOWAReplyText94462 dir=ltr>
<DIV dir=ltr><FONT color=#000000 size=2></FONT> </DIV></DIV>
<DIV dir=ltr><FONT size=2>... of this sequence, are the sequence
itself:</FONT></DIV>
<DIV dir=ltr><FONT size=2></FONT> </DIV>
<DIV dir=ltr><FONT
size=2>1,3,2,6,4,12,8,24,16,48,32,96,64,192,128,384,256,768,512,1536,1024,3072,
...</FONT></DIV>
<DIV dir=ltr><FONT size=2></FONT> </DIV>
<DIV dir=ltr><FONT size=2>This is always true if you interleave sequences (1)
and (2) like that:</FONT></DIV>
<DIV dir=ltr><FONT size=2></FONT> </DIV>
<DIV dir=ltr><FONT size=2>(1) a 2a 4a 8a 16a
32a 64a 128a ...</FONT></DIV>
<DIV dir=ltr><FONT size=2>(2) b 2b 4b 8b
16b 32b 64b 128b ...</FONT></DIV>
<DIV dir=ltr><FONT size=2></FONT> </DIV>
<DIV dir=ltr><FONT size=2>Above, we have a=1 and b=3</FONT></DIV>
<DIV dir=ltr><FONT size=2></FONT> </DIV>
<DIV dir=ltr><FONT size=2>The sequence is a mix of A000079:</FONT></DIV>
<DIV dir=ltr><FONT
size=2>1,2,4,8,16,32,64,128,256,512,1024,2048,4096,8192,</FONT></DIV>
<DIV dir=ltr><FONT size=2></FONT> </DIV>
<DIV dir=ltr><FONT size=2>and A007283:</FONT></DIV>
<DIV dir=ltr><FONT size=2>3,6,12,24,48,96,
192,384,768,1536,3072,6144,12288,</FONT></DIV>
<DIV dir=ltr><FONT size=2></FONT> </DIV>
<DIV dir=ltr><FONT size=2>... which are both their own first
differences.</FONT></DIV>
<DIV dir=ltr><FONT size=2></FONT> </DIV>
<DIV dir=ltr><FONT size=2>Is this old hat?</FONT></DIV>
<DIV dir=ltr><FONT size=2></FONT> </DIV>
<DIV dir=ltr><FONT size=2>----------------</FONT></DIV>
<DIV dir=ltr><FONT size=2></FONT> </DIV>
<DIV dir=ltr><FONT size=2>The sequence below is it's own |fourth absolute
differences| :</FONT></DIV>
<DIV dir=ltr><FONT size=2></FONT> </DIV>
<DIV dir=ltr><FONT size=2>1 1 1 1 2 2 2 2 4 4 4 4 8 8 8 8 16 16 16 16 32 32 32
32 64 64 64 64 ...</FONT></DIV>
<DIV dir=ltr><FONT size=2></FONT> </DIV>
<DIV dir=ltr><FONT size=2>I'm looking for less trivial ones...</FONT></DIV>
<DIV dir=ltr><FONT size=2>Best,</FONT></DIV>
<DIV dir=ltr><FONT size=2>E.</FONT></DIV>
<DIV dir=ltr><FONT size=2></FONT> </DIV>
<DIV dir=ltr><FONT size=2></FONT> </DIV></DIV>
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