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Re: Finding pairs of numbers that meet a specific criteria
Posted:
Nov 3, 2011 6:25 AM
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Thanks Musicgold for that fascinating problem. I have been exploring the
sequence formed by the differences between the smaller numbers in consecutive
pairs, beginning 1,2,1,2,2...
I used a computer to check through the first 100000 numbers and the they only
contained only 1s and 2s and did not contain 2,2,1 or 1,1. Also, the ratio of 2s
to 1s appeared to tend towards the golden mean. If so, then the nth pair would
tend towards (((1+?5)/2)n,((1+?5)/2)n+n-1).
Can anyone offer a proof or disproof?
----- Original Message ----
From: musicgold <discussions@mathforum.org>
To: discretemath@mathforum.org
Sent: Wednesday, 2 November, 2011 14:34:03
Subject: Re: Finding pairs of numbers that meet a specific criteria
Angela,
Brilliant! Yes, it seems to be the solution. I did not occur to me.
Thanks.
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