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        riddles >> easy >> sequence
        
(Message started by: puzzlecracker on Feb 21^st, 2005, 9:38am)

Title: sequence
Post by puzzlecracker on Feb 21^st, 2005, 9:38am

what is the next number in the sequence?

1, 2, 5, 14, 41, ___

Title: Re: sequence
Post by THUDandBLUNDER on Feb 21^st, 2005, 10:01am

Just out of curiosity, where did you get this puzzle?

Title: Re: sequence
Post by rmsgrey on Feb 21^st, 2005, 10:27am

122

Title: Re: sequence
Post by THUDandBLUNDER on Feb 21^st, 2005, 11:01am

on 02/21/05 at 10:27:12, rmsgrey wrote:

122

Not worth hiding, eh?

Title: Re: sequence
Post by Sameer on Feb 21^st, 2005, 12:48pm

::
[hide] a(n)=a(n-1)*3-1
giving 122 [/hide]
::

Title: Re: sequence
Post by puzzlecracker on Feb 21^st, 2005, 1:14pm

on 02/21/05 at 10:01:36, THUDandBLUNDER wrote:

Just out of curiosity, where did you get this puzzle?

some interview I think...

have you also seen this question?

Title: Re: sequence
Post by JocK on Feb 21^st, 2005, 2:35pm

The next number in the sequence 1, 2, 5, 14, 41, ?

That's easy: 122. And the number thereafter is 366.

Title: Re: sequence
Post by THUDandBLUNDER on Feb 22^nd, 2005, 1:09am

on 02/21/05 at 13:14:16, puzzlecracker wrote:

have you also seen this question?

Not this exact question.
But I think it is too easy, even for Easy.
T(n) = 3T(n-1) - 1

on 02/21/05 at 14:35:20, JocK wrote:

And the number thereafter is 366.

Only during a leap year. :P

Title: Re: sequence
Post by rmsgrey on Feb 22^nd, 2005, 5:42am

on 02/21/05 at 11:01:29, THUDandBLUNDER wrote:

Not worth hiding, eh?

Not while the hide tags are still offline - and a naked answer like that doesn't give much away - but stil allows others to check their guesses against mine :)

Title: Re: sequence
Post by JocK on Feb 22^nd, 2005, 11:57am

on 02/22/05 at 01:09:51, THUDandBLUNDER wrote:

Only during a leap year. :P

No, always... Obviously the sequence asked for is the sequence defined by the property that its generating function is the same as its continued fraction:

1, 2, 5, 14, 41, 122, 366, 1103, 3332, 10078, 30503, 92360, 279722, 847283

on 02/22/05 at 01:09:51, THUDandBLUNDER wrote:

[..] I think it is too easy, even for Easy.

I think it is too hard for Easy..! ;)

Title: Re: sequence
Post by THUDandBLUNDER on Feb 23^rd, 2005, 6:24am

on 02/22/05 at 11:57:48, JocK wrote:

No, always... Obviously the sequence asked for is the sequence defined by the property that its generating function is the same as its continued fraction:

Yes, a typically perplexing puzzlecracker poser. ::)

.

Title: Re: sequence
Post by Sjoerd Job Postmus on Mar 4^th, 2005, 5:45am

on 02/21/05 at 14:35:20, JocK wrote:

The next number in the sequence 1, 2, 5, 14, 41, ?

That's easy: 122. And the number thereafter is 366.

This makes me wonder how you arrive to 366.

since someone stated that a(n) = a(n-1)*3 - 1, the first list follows logically, up to the 122.
The 366 however, does not follow logically.
When I fill in 122*3 - 1, 365 follows, not 366.
Following the formula, the next would be 1094.

How did you derive your own answer, as I do not understand.

Title: Re: sequence
Post by rmsgrey on Mar 4^th, 2005, 6:51am

on 03/04/05 at 05:45:53, Sjoerd Job Postmus wrote:

He "explained" his reasoning in a later post:

on 02/22/05 at 11:57:48, JocK wrote:

Mathworld (http://mathworld.wolfram.com) is a good source for definitions of mathematical terms: Generating Function (http://mathworld.wolfram.com/GeneratingFunction.html) and Continued Fraction (http://mathworld.wolfram.com/SimpleContinuedFraction.html)

Title: Re: sequence
Post by Grimbal on Mar 4^th, 2005, 8:41am

You can also have a look at:
http://www.research.att.com/cgi-bin/access.cgi/as/njas/sequences/eisA.cgi?Anum=A088355