Random, hopefully simple, number sequence

[mith]

Find the last term of this sequence. I will post more terms at the beginning as hints, if needed. I will not confirm or deny answers without reasoning.

...72, 120, 48, 72, 24, 16, _

[DrJones]

...72, 120, 48, 72, 24, 16, _

All the numbers are even. Is it a coincidence?
Let's chop the sequence
...36, 60, 24, 36, 12, 8, _
Mithosis...
...18, 30, 12, 18, 6, 4, _
Separation...
...9, 15, 6, 9, 3, 2, _

Mmmm... odd numbers appeared.
How funny !!
I thought A(n+1) in the sequence could be |A(n-1)-A(n)|, but that's wrong with the last numbers

Aha! I got it! (I guess)
-8

[mith]

Any reasoning for that guess?

[cubestudent]

i have two semilogical guesses:


if the first hint# is 160, i think the answer's 0
but if it's 168, i think the answer's -8



[This message has been edited by cubestudent (edited 03-19-2002 09:25 PM).]

[mith]

No, the hint number is not 160.

[cubestudent]

then:

is it 168?

[mith]

Yes

[cubestudent]

sorry to be so pesiferous, mith. . .

but did you get my e-mail?

[mith]

where did you send it?

[cubestudent]

mithrandir@spl.net

oops. it'll be from poetcoder@yahoo.com

[This message has been edited by cubestudent (edited 03-19-2002 09:49 PM).]

[mith]

check the address. it's mithrandir@spl.at

[cubestudent]

crap.

i'm sorry.

i misread your add.

umm. *blushess*

well, the subject was basically a request to be added to the replacement player list for the Wheel of Time Mafia game.

again, sorry.

[mith]

you could have just posted i'll make a note somewhere, i'm sure there will be someone that needs replacing.

now will someone solve this?

[DrJones]

This is my reason:
There are two sequences mixed, one in the even and another in the odd elements. The value of an element in the even part of the sequence is the addition of its adjacent ones. So 16 = 24 + x => x= -8

There's something strange in all of this:
In the odd part of the sequence, it looks like it decreases each step by 24, but in the final step, it decreases 32! Why?

Ups! Perhaps I forget to put ink in my pen...

[mith]

Incorrect. The sequence does not have two parts.

Hint added to beginning:

...168, 72, 120, 48, 72, 24, 16, _

Second hint: The sequence has no beginning, and the blank is the last term in the sequence. I could have posted it in the other direction, but I think it would have been easier that way.



[This message has been edited by mith (edited 03-20-2002 09:01 PM).]

[DrJones]

In that case, let's try another thing:
If the next hint is 96, the last term is 0

[mith]

The next hint is not 96.

[mith]

Another hint added to the beginning: ...312, 168, 72, 120, 48, 72, 24, 16, _

[This message has been edited by mith (edited 03-20-2002 09:02 PM).]

[cubestudent]

perhaps. . .


the next hint will be: 432?

[mith]

Not even close.

[DrJones]

If next hint is 72, the last term is 72

Hey! I guess I had to try it.

[mith]

Nope. This sequence is evil, heh. It really is simple, though.

[mith]

Third hint number: ...120, 312, 168, 72, 120, 48, 72, 24, 16, _

[Sofis]

Oh, come on. People. It's obvious. Look:

[mith]

I was wondering when someone was going to point that out. Not sure why I put "random" in the title. *~shrug~*

The answer is not 42.

[mith]

Fourth hint number: ...408, 120, 312, 168, 72, 120, 48, 72, 24, 16, _

If no one gets this soon I may have to save it for a potpourri or something

[mith]

One last bump...

[CrystyB]

I'll look into it at home. Please be prepared to bump it one more time if i DON'T solve it today!

[CrystyB]

Damn! I thought i solved it...
... 120 216 96 168 72 120 48 72 24 24 0

[mith]

Shall I put this one to rest, or save it for the next potpourri?

[mith]

Ok, I will post the solution, but not the reasoning. Maybe someone can figure *that* out.

5

[mith]

No one? I'm disappointed, it's not *that* hard.

[CrystyB]

right. Yours and Chuck's are the easiest!

[mith]

*~bump~*

No one has gotten this yet? This was a prime opportunity for someone to restore my faith in humanity. I guess it doesn't make much difference anyway.

Repost of sequence, in the more normal order:

5, 16, 24, 72, 48, 120, 72, 168, 312, 120, 408,...

[cubestudent]

your subtle hints are no match for my thick skull.

[Athene]

312?

[mith]

*~gasp~* Has someone finally got it?

[Athene]

Then the next ones would be 168, 360, 600, 672.

Those are the differences of squared prime numbers, eg. 5=3²-2², 16=5²-3², 24=7²-5².