What is the next number in this series?

[Slick itler]

1,2,8, ...

[quasi]

On Wed, 8 Feb 2012 20:47:16 -0800 (PST), Slick itler
<toser...@gmail.com> wrote:

>1,2,8, ...

Anything it wants to be.

quasi

[Don Stockbauer]

On Feb 8, 10:54 pm, quasi <qu...@null.set> wrote:
> On Wed, 8 Feb 2012 20:47:16 -0800 (PST), Slick itler
>

> <toseriou...@gmail.com> wrote:
> >1,2,8, ...
>
> Anything it wants to be.
>
> quasi

Anything YOU want it to be.

[Bill Taylor]

On Feb 9, 6:45 pm, Don Stockbauer <donstockba...@hotmail.com> wrote:

> > >1,2,8, ...
>
> > Anything it wants to be.

If it's a random sequence (NOT a series I hope).

> Anything YOU want it to be.

If it's a choice sequence.

And if it's a law-like sequence, then the next number is

[Tim Little]

On 2012-02-09, Bill Taylor <wfc.t...@gmail.com> wrote:
[...]
>> > >1,2,8, ...
[...]

> And if it's a law-like sequence, then the next number is

Anything you want it to be.


--
Tim

[Jussi Piitulainen]

Tim Little writes:

> On 2012-02-09, Bill Taylor wrote:
> [...]
> >> > >1,2,8, ...
> [...]
> > And if it's a law-like sequence, then the next number is
>
> Anything you want it to be.

Wait, what? I thought it was anything _quasi_ wants it to be.

I'd like it to be 1073741824, if I may.

[José Carlos Santos]

On 09-02-2012 4:47, Slick itler wrote:

> 1,2,8, ...

Who wants to know?

Best regards,

Jose Carlos Santos

[David C. Ullrich]

On Wed, 8 Feb 2012 20:47:16 -0800 (PST), Slick itler

<toser...@gmail.com> wrote:

>1,2,8, ...

Either a_3 or a_4, depending on which convention
you prefer.

[Jim Burns]

You have much higher grade numbers than I do.
Mine just sort of sit there, not wanting, not doing
much of anything. Lifeless, one might almost say.

Where do you get yours? Are they the luxury brand?
I usually get generic.

[Jim Burns]

On 2/9/2012 12:45 AM, Don Stockbauer wrote:
> On Feb 8, 10:54 pm, quasi<qu...@null.set> wrote:
>> On Wed, 8 Feb 2012 20:47:16 -0800 (PST), Slick itler
>> <toseriou...@gmail.com> wrote:

>>> 1,2,8, ...
>>
>> Anything it wants to be.
>

> Anything YOU want it to be.

Wait a minute. Is this an accounting question?
I could never get the hang of accounting.

[AP]

On Wed, 8 Feb 2012 20:47:16 -0800 (PST), Slick itler

<toser...@gmail.com> wrote:

>1,2,8, ...
why not 64 ?
because 2^((n-1)n/2)
is 1 for n=1
is 2 for n=2
is 8 for n=3
is 64 for n=4

[Butch Malahide]

On Feb 9, 9:48 am, AP <marc.picher...@wanadoo.fr.invalid> wrote:
> On Wed, 8 Feb 2012 20:47:16 -0800 (PST), Slick itler
>

> <toseriou...@gmail.com> wrote:
> >1,2,8, ...
>
>  why not 64 ?
> because 2^((n-1)n/2)
> is 1 for n=1
> is 2 for n=2
> is 8 for n=3
> is 64 for n=4

Why not 128 ?
because 2^((2^n)-1)
is 1 for n=0
is 2 for n=1
is 8 for n=2
is 128 for n=3

[quasi]

Sure, that works.

An OEIS search also yields this one

(2n)!!

as well as more than 2000 other sequences matching the
initial terms 1,2,8.

But in fact, for any value of a_4, the sequence

1,2,8,a_4

can be matched by an appropriately chosen expression for a_n.

quasi

[Jussi Piitulainen]

Mine's a_n = a_{n - 1} ^ (a_{n - 2} + a_{n - 1}), after 1, 2, of
course. So the 8 is 2^(1 + 2) and the next number is 8^(2 + 8).

[quasi]

On Thu, 09 Feb 2012 10:29:39 -0500, Jim Burns <burn...@osu.edu>
wrote:

Just let them know they're free to roam.

I believe in giving numbers "rights".

Or at least _some_ rights. For my real numbers, I let them
travel anywhere as long as they stay in line.

quasi

[Dan Christensen]

On Feb 8, 11:47 pm, Slick itler <toseriou...@gmail.com> wrote:
> 1,2,8, ...

If this is just a test question, you are probably meant to be
multiplying by ascending powers of 2 with the first term being 1.

1 1x2=2 2x4=8 8x8=64 64x16=1024 1024x32=32768 ...

If this is a "real world" question, all bets are off!

Dan

[Tonico]

On Feb 9, 5:48 pm, AP <marc.picher...@wanadoo.fr.invalid> wrote:
> On Wed, 8 Feb 2012 20:47:16 -0800 (PST), Slick itler
>

> <toseriou...@gmail.com> wrote:
> >1,2,8, ...
>
>  why not 64 ?
> because 2^((n-1)n/2)
> is 1 for n=1
> is 2 for n=2
> is 8 for n=3
> is 64 for n=4

Hmmm....what about 19? Because 2 - 1 = 1, 8 - 2 = 1 + 5 = 6, so
_obviously_ the next difference is 6 + 5 = 11...

No, wait! What about 36? Because 2 - 1 = 1 = first perfect natural
number, 8 - 2 = 6 = second perfect number, so _obviously_ x - 8 = 28 =
third perfect number, and thus x = 36...!

No, wait! What about 1? Because this is _obviously_ the cyclic
sequence 1,2,8,1,2,8,...

No, wait! What about 64? Because 2 = 2*1, 8 = (2^2)*2, so the next
element is _obviously_ (2^3)*8 = 64...

No, wait...

Tonio

[Michael Stemper]

That doesn't sound very complex. In fact, it sounds completely natural.

--
Michael F. Stemper
#include <Standard_Disclaimer>
You can lead a horse to water, but you can't make him talk like Mr. Ed
by rubbing peanut butter on his gums.

[K_h]

"Slick itler" <toser...@gmail.com> wrote in message
news:31d243d9-6d09-4da5...@lr19g2000pbb.googlegroups.com...
> 1,2,8, ...

The next number should be 19, if you use the collocation method. Under that
method, the polynomial is:

P(x) = (5/2)x^2 - (3/2)x + 1.

+

[AP]

it was only for show an example....

[David R Tribble]

>>1,2,8, ...

Jussi Piitulainen wrote:
> I'd like it to be 1073741824, if I may.

I vote for zero.

[G. A. Edgar]

In article
<31d243d9-6d09-4da5...@lr19g2000pbb.googlegroups.com>,

Slick itler <toser...@gmail.com> wrote:

> 1,2,8, ...

Try the Encyclopedia of Integer Sequences.
https://oeis.org/
It found many answers to your question: a sequence of interest for some
reason that begins 1,2,8. In fact, there are 2,210 matches. The
first one that comes up: A000165, the "double factorial (2n)!!", where
0!! = 1, 2!! = 2, 4!!=8. If THAT is your sequence, then the next one is
6!!=48

--
G. A. Edgar http://www.math.ohio-state.edu/~edgar/

[Helmut Richter]

On Thu, 9 Feb 2012, David R Tribble wrote:

> Subject: Re: What is the next number in this series?

It is certainly true that any number can be the next in a sequence. But it is
a premature jump to conclusions to say that such quizzes are meaningless for
mathematicians. Such a quiz can be both a useful training of mathematical
skills and an assessment of such skills.

Usefulness: When the numbers in a sequence are the values of a well-defined
(but not by simple expression or by recursion formula) function, for instance
the solution to a combinatorial problem (e.g. maximal number of pieces into
which a pizza can be cut with /n/ straight-line cuts), solving such a quiz
could be the first step for finding a more useful representation of that
function -- of course one has to prove afterwards that it is indeed the
intended function.

Assessment: The problem is solved if the test person comes up within a given
time (some minutes) with the next number *and* the underlying law. The law
must not be arbitrary in the sense that would have worked with any other
continuation as well. E.g. a law "the fourth and every subsequent element is
zero" is arbitrary because it would have worked with any other number. Giving
the law by a polynomial is allowed but it will usually not be possible to give
the polynomial and the next number within a few minutes.

Of course, more than one solution is possible, and if the problem is well put,
at least one of them is reasonably simple, to wit the one the inventor
intended. Because of the short sequence given here, several such solutions
have been proposed. A test person would have passed the test with presenting
any of them, but no test person could have profited from the fact that
sequences as defined in mathematics can have any continuation.

--
Helmut Richter

[Bill Taylor]

> Or at least _some_ rights. For my real numbers, I let them
> travel anywhere as long as they stay in line.

God said
"Let there be numbers"
And there WERE numbers.
Odd and even created he them.
He said to them "Go forth and multiply".
And he commanded them to keep the laws of Induction.

-- Biblical Bill

[Pfs...@aol.com]

On Wed, 8 Feb 2012 20:47:16 -0800 (PST), Slick itler
<toser...@gmail.com> wrote:

>1,2,8, ...

This isn't a math question, it's a psychology question.
It's easy to write an infinite family of math solutions, each as
correct as any other.
The "correct answer is the one the questioner expects to see!

[quasi]

Or equivalently, stay well ordered.

But some pairs discovered that besides adding, they could also
subtract, and the results were sometimes quite negative.

Then divisions began among the them, leading some numbers
to split into two parts, partitioned by a bar.

It was the only rational thing to do.

But some were not so rational.

Initially, it was seen as just a few radical elements,
defiantly irrational.

But over time, it became apparent that rationality was the
rare exception, to the point where if you met a number at
random, it was almost sure to be irrational.

Still, throughout the realm, total order was maintained.

But some numbers had more roots than others, and in an effort
to be more equitable, new roots were imagined, then actually
constructed. The usual interactions between pairs of numbers
ensued, with the results often being quite complex.

quasi

[Bill Taylor]

On Feb 12, 7:57 am, quasi <qu...@null.set> wrote:

> But some pairs discovered that besides adding, they could also
> subtract, and the results were sometimes quite negative.
>
> Then divisions began among the them, leading some numbers
> to split into two parts, partitioned by a bar.
>
> It was the only rational thing to do.
>
> But some were not so rational.
>
> Initially, it was seen as just a few radical elements,
> defiantly irrational.
>
> But over time, it became apparent that rationality was the
> rare exception, to the point where if you met a number at
> random, it was almost sure to be irrational.
>
> Still, throughout the realm, total order was maintained.
>
> But some numbers had more roots than others, and in an effort
> to be more equitable, new roots were imagined, then actually
> constructed. The usual interactions between pairs of numbers
> ensued, with the results often being quite complex.

Very good!

I'm sure you must know that when Noah released the animals
onto dry land again, he said "Go forth and multiply!"
But that two little snakes came up to him and said,
"Please sir, we can't - we're adders!"

But Noah had np problem - he just put them down
on log tables!

-- Boring old Bill

(one of the decreasing few who still se the point
of this joke...)

[Risto Kauppila]

09.02.2012 06:54, quasi kirjoitti:
> On Wed, 8 Feb 2012 20:47:16 -0800 (PST), Slick itler
> <toser...@gmail.com> wrote:
>
>> 1,2,8, ...
>

> Anything it wants to be.
>

> quasi

Right! There are an infinite number of sequences starting like that.
If an analytic or number-theoretic expression is what is wanted, the
question should be formulated otherwise.

Rike

[Risto Kauppila]

Sorry, obviously I made a bad grammatical error. My english is poor.

Rike

[Richard Henry]

On Feb 8, 8:47 pm, Slick itler <toseriou...@gmail.com> wrote:
> 1,2,8, ...

3, 81, 4 ...

Obviously.

(1^2, 2, 2^3, 3, 3^4, 4 ...)

A better version of this problem is "How many numbers can you justify
as the next number in this sequence? Show your work".