[seqfan] Re: Puzzle

Bob Selcoe rselcoe at entouchonline.net
Wed Jan 21 01:41:27 CET 2015


Hi David and seqfans,

r = 1/j, j >= 1 certainly works.  We can always reach j, take next the 
reciprocal 1/j, then continue adding until we reach 1.

It seems likely that all fractions will also work, is this true?

Best,
Bob Selcoe

--------------------------------------------------
From: "David Wilson" <davidwwilson at comcast.net>
Sent: Tuesday, January 20, 2015 6:04 PM
To: "math-fun" <math-fun at mailman.xmission.com>; "Sequence Fanatics 
Discussion list" <seqfan at list.seqfan.eu>
Subject: [seqfan] Puzzle

> Choose any real r >= 0.
>
>
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> Starting with n = 1, on the first step add r, on subsequent steps either 
> add
> r or take the reciprocal as you choose.
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> For example, if r = 1/4, we can generate the sequence
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> 1, 5/4, 3/2, 7/4, 2, 1/2, 3/4, 1.
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> For which r is it possible to return to 1 as does this sequence?
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>
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> 



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