What follows is a Fibonacci sequence done in various bases and all double digit numbers have been added together (don't ask why). The pattern repeats in every sequence; this is denoted by the numbers in ellipsis.
What are some possible causes for this repetition? I speculate that it would be the exception to the rule that numbers do not repeat themselves. I can entertain that idea by presenting a challenge to my readership (all two of you) - provide me with a calculation that I cannot break down into a pattern. Certain known infinite decimals are off limits (such as pi, phi, square roots of primes, or other known irrational numbers).
base 9
1123585(5)
22462(2)
336178(78)
4484(4)
552718(18)
664268(68)
776538(38)
base 8
11235167(67)
224632575(5)
336213474(4)
441564373(3)
553145272(2)
665426171(1)
base 7
1123521341565(5)
224644262(2)
336(336)
44268(8)
5543145325161(1)
base 6
11235331454432522415
224151(1)
331454(4)
44325(2)
base 5
1123141(1)
2242(2)
3321343(3)
base 4
11232(2)
22131(1)
base 3
112(112)
Chuck - 6/14/2006 11:29:00 PM
Anonymous - 6/13/2006 03:38:08 PM
I just can't figure out why its 24. seems odd. - from Chuck-onacci
Well, let's look at some number sets:
base 10
112358437189887641562819 - 24
224617865279775382134729 - 24
33696639 - 8
448325731459551674268549 - 24
551674268549448325731459 - 24
66393369 - 8
775382134729224617865279 - 24
887641562819112358437189 - 24
9 - 1
Clearly there is a relationship to the numbers 3 and 8 here. Three at 2 multiples is a 8 set sequence. Three multiplied by eight is 24, the other sequence.
It appears the other bases all have their own sequences. I find it interesting that the predominant pattern tends to begin quite orderly and approaches apparant disorder before returning to order.
Itchy_turd - 6/15/2006 07:12:00 PM
Am I the only person that remembers learning about Fibonacci on an episode of "Mathnet" on Square One on PBS as a kid?
Also, I caught Chuck's clever reference to "All your base..."
- 6/16/2006 06:09:00 AM
So, was this inspired by the DaVinciCode or what? :)
See ya, maybe,
your non-local neighborhood drug dealer
Chuck - 6/16/2006 12:12:00 PM
No, not DaVinciCode. I haven't read it yet, nor will I anytime soon. My reading list is populated from now until the end of next year with titles like:
Disciples of Destruction - Charles W. Sutherland
Wonderdog - Inman Majors
A Selfish Man - William Brandon
a stack of Bill Bryson books
and I still have to finish reading The Third Chimpanzee by Jared Diamond.
This is simply an obsession I have to tweak numbers and rejoice in revealing some pattern or shortcut. In doing this I learned how to rapidly calculate base conversions close to the number 10.
Chuck - 6/16/2006 12:16:00 PM
I vaguely recall the Electric Company possibly teaching some math - but that was it. I was never enriched by Square One. :(
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