Collatz related sequence...

[N. J. A. Sloane]

Dear Seqfans,  This message just came in.  Would one
of you kindly reply to him (and tell the list you are
doing so)?
I'm about to leave on a trip.
NJAS

>From jim.cp at zonnet.nl  Thu Feb  3 07:15:24 2005
>Delivered-To: njas at research.att.com
>To: njas at research.att.com
>Subject: Collatz related sequence...
>Date: Thu, 03 Feb 2005 13:14:49 +0100
>From: "Jim Caprioli" <jim.cp at zonnet.nl>
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>Dear Sir,
>
>How can I query your database to find the following sequence??
>
>Table [
>IntegerPart[Mod[x - 1 , 2]/1] +
>2 IntegerPart[Mod[x - 2 , 4]/3] +
>4 IntegerPart[Mod[x , 8] / 7] +
>8 IntegerPart[Mod[x - 4 , 16] / 15] +
>16 IntegerPart[Mod[x + 4, 32]/31] +
>32 IntegerPart[Mod[x - 12, 64]/63] +
>64 IntegerPart[Mod[x + 20, 128]/127] +
>128 IntegerPart[Mod[x - 44, 256]/255]
>
>,
>{x, 1, 235}]
>
>{2, 1, 8, 1, 2, 1, 4, 1, 2, 1, 32, 1, 2, 1, 4, 1, 2, 1, 8, 1, 2, 1, 4, 1,  
>2, 1, 16, 1, 2, 1, 4, 1, 2, 1, 8, 1, 2, 1, 4, 1, 2, 1, 128, 1, 2, 1, 4, 1,  
>2, 1, 8, 1, 2, 1, 4, 1, 2, 1, 16, 1, 2, 1, 4, 1, 2, 1, 8, 1, 2, 1, 4, 1,  
>2, 1, 32, 1, 2, 1, 4, 1, 2, 1, 8, 1, 2, 1, 4, 1, 2, 1, 16, 1, 2, 1, 4, 1,  
>2, 1, 8, 1, 2, 1, 4, 1, 2, 1, 64, 1, 2, 1, 4, 1, 2, 1, 8, 1, 2, 1, 4, 1,  
>2, 1, 16, 1, 2, 1, 4, 1, 2, 1, 8, 1, 2, 1, 4, 1, 2, 1, 32, 1, 2, 1, 4, 1,  
>2, 1, 8, 1, 2, 1, 4, 1, 2, 1, 16, 1, 2, 1, 4, 1, 2, 1, 8, 1, 2, 1, 4, 1,  
>2, 1, 0, 1, 2, 1, 4, 1, 2, 1, 8, 1, 2, 1, 4, 1, 2, 1, 16, 1, 2, 1, 4, 1,  
>2, 1, 8, 1, 2, 1, 4, 1, 2, 1, 32, 1, 2, 1, 4, 1, 2, 1, 8, 1, 2, 1, 4, 1,  
>2, 1, 16, 1, 2, 1, 4, 1, 2, 1, 8, 1, 2, 1, 4, 1, 2, 1, 64}
>
>This sequence plays a role in the solution to the Collatz problem.
>
>If your eyes don't hurt when you see amateur math, have a look at
>http://jimcaprioli.blogspot.com
>
>I suspect that there are an infinite number of formulas which generate the  
>sequence ( infinite one ) above. A more compact formula than I have would  
>be very helpful. That is why I queried the database.
>
>Thanks.
>
>have you seen the 0 at number 175? It is where 512 fits, and so on.
>-- 
>jim caprioli
>