Need help...

ninelven

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4, 2, 3, 2, 3, 2, 5, 2, 3, 2, 4, 2, 3, 2, 6, 2, 3, 2, 4, 2, 3, 2, 5......

Difficulty I'm having is due to it becoming more complex (though predictably so) as n -> infinity.

It is modelling the number of times 2 will divide X evenly, where X is in {36N-20}.

Any ideas?
 
I assume you are supposed to find a closed form expression for that number as a function of N right? (In which case modeling is a strange term to use.)
 
God I have no clue ... you have to use modular arithmetic, that much is clear. (My intuition says there is some parallel with error correction polynomials ... meh, this stuff was too long ago for me and I didn't even understand it well enough for anything else but the exam at the time.)
 
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Yeah, its fairly difficult... appears to be both harmonic and recursive. But if I ever figure it out, it should be well worth the trouble :). Any ideas appreciated, even wild ass guesses.
 
Figured something out about the structure...

It is the sum of the series(es).. series of series if you prefer of: 2^((2^P)*N - 1) When the sums are represented in binary and added together in base 10.

EX:
+01010101010101010101...
+00010001000100010001...
+00000001000000010000...
+00000000000000010000...
=01020103010201040102

But that was fairly obvious to begin with.... and is still quite cumbersome. :/
 
Each series adds up to a number as n approaches infinity for each p which, when they are represented in binary form and added together in base 10, are a solution (to a superset of what I was originally interested in). Not exactly what I was looking for, but its enough progress to make me happy :).
 
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Doesn't really sound like the solution a teacher would be looking for ... it's not closed form either.
 
Are you quite sure you got the sequence you're trying to model right any way? I found a way to get wolfram alpha to spit it out :

http://www.wolframalpha.com/input/?i=ntz(36x-20)

The one you had in your first post was plain wrong ... and it seems to simply repeat indefinitely, although I can't really prove that (which is the problem with modeling in the first place, this isn't physics ... inductive reasoning can only give you a conjecture, you're looking for a solution so you would still need proof).
 
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MfA said:
Doesn't really sound like the solution a teacher would be looking for ... it's not closed form either.

It's not for a teacher.... it's a small part of proof for a certain conjecture I'm working on. The reason it is important for my proof is it allows me to understand the underlying function in a meaningful way.

MfA said:
inductive reasoning can only give you a conjecture
That isn't true; there are plenty of inductive proofs in mathematics.
 
The method of induction in math is not inductive reasoning, you aren't using the method of induction ... you are using inductive reasoning.
 
I know that...

FFS, I'm not going to get into an argument over my knowledge of abstract mathematics.... It is more than satisfactory to meet my own needs.
 
9*64 = 1001000000

So all bits of 9N-5 lower than 6 will be identical for N=x and N=x+64. If 9N-5 for N=1...64 does not have a number of trailing zeros higher than 5 the sequence of ntz(9N-5) is guaranteed to repeat from 64 onward. The highest number of trailing zeros for N=0...64 is for N=61 (found by exhaustive search) 9*61-5 = 1000100000 has 5 trailing zeros ... so the sequence repeats indefinitely.

Fucking hideous proof, but proof nonetheless.
 
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