# Recursive sequence question Watch

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#2

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**jamie092**)...

I think you've gone wrong in your example in going from g(40)+7 to g(13)+6.

**Edit:**Aside from the "+1" bit this relates to the Collatz or 3+1 conjecture

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I just used g(3n+1)=g(n)-1 for that step, I can't see how that's wrong (I'm not saying it's not wrong, just that I'm not feeling very awake ^^)

Yeah I looked at that wikipedia page but I didn't really get anywhere because all other examples of recursive sequences define the nth term in terms of the (n-1)th term.

That Collatz conjecture does look interesting though, I've bookmarked it! :P

Yeah I looked at that wikipedia page but I didn't really get anywhere because all other examples of recursive sequences define the nth term in terms of the (n-1)th term.

That Collatz conjecture does look interesting though, I've bookmarked it! :P

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#4

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I just used g(3n+1)=g(n)-1 for that step, I can't see how that's wrong (I'm not saying it's not wrong, just that I'm not feeling very awake ^^)

**jamie092**)I just used g(3n+1)=g(n)-1 for that step, I can't see how that's wrong (I'm not saying it's not wrong, just that I'm not feeling very awake ^^)

If we paraphrase the definition of g(n) for n odd, it says:

g(n) is defined to be g(3n+1) + 1.

From this you cannot infer g(3n+1) is defined to be g(n) - 1

The "=" sign is perhaps misleading in this context.

Yeah I looked at that wikipedia page but I didn't really get anywhere because all other examples of recursive sequences define the nth term in terms of the (n-1)th term.

That's the basic form of recursion, the nth term is defined in terms of the (n-1)th. There is a computer algorithm further down that shows it nicely.

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(Original post by

That's not something you can validly do.

If we paraphrase the definition of g(n) for n odd, it says:

g(n) is defined to be g(3n+1) - 1.

From this you cannot infer g(3n+1) is defined to be g(n) + 1

The "=" sign is perhaps misleading in this context.

**ghostwalker**)That's not something you can validly do.

If we paraphrase the definition of g(n) for n odd, it says:

g(n) is defined to be g(3n+1) - 1.

From this you cannot infer g(3n+1) is defined to be g(n) + 1

The "=" sign is perhaps misleading in this context.

I do see what you mean though I guess you can't define two things as each other.

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#6

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But if I have to use the definition that way around, then I can only calculate g(23) from terms above it i.e g(23)=g(70) +1 and then I'd have to keep going, the only way to get in terms of lower terms would be to use that g(even)=g(even/2).

**jamie092**)But if I have to use the definition that way around, then I can only calculate g(23) from terms above it i.e g(23)=g(70) +1 and then I'd have to keep going, the only way to get in terms of lower terms would be to use that g(even)=g(even/2).

You started at g(23) and after several steps got to g(40), which leads you to g(20), to g(10), to g(5), and then up to g(16)....

The process goes up and down, until you get to 1 - at least according to the Collatz Conjecture.

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(Original post by

That's prefectly correct.

You started at g(23) and after several steps got to g(40), which leads you to g(20), to g(10), to g(5), and then up to g(16)....

The process goes up and down, until you get to 1 - at least according to the Collatz Conjecture.

**ghostwalker**)That's prefectly correct.

You started at g(23) and after several steps got to g(40), which leads you to g(20), to g(10), to g(5), and then up to g(16)....

The process goes up and down, until you get to 1 - at least according to the Collatz Conjecture.

I got that g(2^n)=n+1 from the even part which is kind of nice. And then numbers such that n=2^m where n=3k+1 are going to be useful.

I was just wondering if that's the only way to do it, number by number, or if I can calculate a formula like T_n=f(n) or something

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#8

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Ah ok then, well thanks a lot!

I got that g(2^n)=n+1 from the even part which is kind of nice. And then numbers such that n=2^m where n=3k+1 are going to be useful.

I was just wondering if that's the only way to do it, number by number, or if I can calculate a formula like T_n=f(n) or something

**jamie092**)Ah ok then, well thanks a lot!

I got that g(2^n)=n+1 from the even part which is kind of nice. And then numbers such that n=2^m where n=3k+1 are going to be useful.

I was just wondering if that's the only way to do it, number by number, or if I can calculate a formula like T_n=f(n) or something

If you can find a formula, you'll be due an honourary Ph.D. at least, I think.

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(Original post by

A lot of work has gone into investigating the Collatz Conjecture, and as it stands, it's still a conjecture.

If you can find a formula, you'll be due an honourary Ph.D. at least, I think.

**ghostwalker**)A lot of work has gone into investigating the Collatz Conjecture, and as it stands, it's still a conjecture.

If you can find a formula, you'll be due an honourary Ph.D. at least, I think.

Thanks for the help anyway

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#10

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Haha ok, well I doubt that's happening any time soon eh =)

Thanks for the help anyway

**jamie092**)Haha ok, well I doubt that's happening any time soon eh =)

Thanks for the help anyway

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