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Capuchin
Feb 19, 2007, 08:05 AM
Here is an interesting number sequence.

It is available on the web so please take it in the spirit it is given, for good fun, and don't look it up.

Here are the first 10 terms:

0, 0, 0, 0, 4, 9, 5, 1, 1, 0,

I ask you to post the next unconfirmed number in the sequence, without explaining why, so that others may have a go.

I will reveal extra numbers if nobody gets the next term in a day or so.
I will also let people know if their term is correct.
On Friday I will give the rule for anybody who is still stuck.

Many thanks for observing these guidelines to maximise everyone's fun :)

Feel free to post thoughts and suspicions though :) - clues will be available if nobody is on the right track

asterisk_man
Feb 19, 2007, 09:19 AM
I'm guessing that the sequence is based on an external data source. i.e. it is not a mathematical function like f(n). Looking at f(n)-f(n-1) and f(n)/f(n-1) reveal no obvious patterns. I'll continue to investigate!

colbtech
Feb 19, 2007, 09:37 AM
Are these the last 10 scores made by English opening batsmen in cricket?

Capuchin
Feb 19, 2007, 09:45 AM
Entertaining guess colbtech

Not right though :)

I don't think I'll comment on mathematical function yet asterisk.

asterisk_man
Feb 19, 2007, 10:51 AM
So hard to investigate something without using Google! :)
Can't be a simple letter/number substitution. No word starts with 4 consecutive same letters. The answer is available on the web so it must not be using any of the sentences that capuchin wrote that would only apply to this forum at this time as a data source.
Since I have nothing better I will make the naïve guess that it is a simple repeating pattern
0, 0, 0, 0, 4, 9, 5, 1, 1,0, 0, 0, 0, 4, 9, 5, 1, 1, 0, 0, 0, 0, 4, 9, 5, 1, 1, 0,
So the next number would be 0? Maybe capuchin will let a hint fly when he tells me I'm wrong :)

Capuchin
Feb 19, 2007, 10:57 AM
Well that wouldn't be very exciting would it :p

I'm going to wait till tomorrow to give a clue.

asterisk_man
Feb 19, 2007, 11:07 AM
So 0 is or is not the next term in the sequence :)

Capuchin
Feb 19, 2007, 11:10 AM
Is not.

asterisk_man
Feb 19, 2007, 11:27 AM
Maybe letter count in some text? But what text would have zero a b c d j and 3*e 9*f 5*g 1*h 1*i ? That's a lot of f for so few e. e should be about 12.7% of the letters so the text would be about 24 characters long but f should only be 2.2% so the text would be about 409 characters long. Based on this inconsistency I'm guessing it isn't letter count or the text is short, about 30 characters and has unusual words.
Just thinking aloud so feel free to tell me your side... if anyone else is working this besides me.

Capuchin
Feb 19, 2007, 11:32 AM
Okay, a mini clue, it's an infinite sequence.

I don't want to give too much away until the other math heads have popped in

asterisk_man
Feb 19, 2007, 11:35 AM
OK. Everyone else must be asleep. I'll try to sit on this one until I find an answer or tomorrow comes around :)

galactus
Feb 19, 2007, 01:04 PM
I only know (I think) because I have seen this before. Is the next number 55?

Capuchin
Feb 19, 2007, 01:26 PM
Hehe yes galactus,

Anyone want to guess the 12th term? :)

(I think that should confuse asterisk man)

asterisk_man
Feb 20, 2007, 07:57 AM
Agreed! Very confused!

Capuchin
Feb 21, 2007, 01:23 AM
0, 0, 0, 0, 4, 9, 5, 1, 1, 0, 55,.

Anyone want to hazard a guess at term 12? :)

asterisk_man
Feb 21, 2007, 07:43 AM
I want to hazard a guess but I can't because I can't figure out a pattern! And the "I think that should confuse asterisk man" comment confuses me most of all :)

Capuchin
Feb 21, 2007, 07:46 AM
I was simply commenting that it going from a nice single digit sequence up to 55 would confuse anybody, especially you as you are putting some effort into it :p

galactus
Feb 21, 2007, 07:47 AM
The 12th term is 55 also. The 13th is 1.

Capuchin
Feb 21, 2007, 07:48 AM
*shakes fist at galactus*

You've given it away now! :P

galactus
Feb 21, 2007, 07:50 AM
I doubt it. The pattern is rather obscure for anyone to find. The only reason I know it is because I seen it several years back. I will stay out of it from here on out. We'll see if anyine gets it. Some bright folks here.

Capuchin
Feb 21, 2007, 07:54 AM
Hehe someone will get it, I was being a little sarcastic with the given it away comment :p

I know someone at my place of work who got it (took them half a day though)

galactus
Feb 21, 2007, 07:55 AM
No worries. I'm not thin-skinned

So there:p :D

asterisk_man
Feb 21, 2007, 08:19 AM
*dim bulb*

Evil dead
Feb 21, 2007, 09:49 AM
0, 0, 0, 0, 4, 9, 5, 1, 1, 0, 55, 55, 1.

Hmm. This is something to do with square root or cube root. The way it shoots up to 55 then straight back down to 1 is quite bemusing.

How ever, what I do know that it is based on Computer Science or some sort of Binary Code.

Capuchin
Feb 21, 2007, 09:55 AM
Hi Evil dead and welcome to the discussion!

Maybe you and asterisk man can shove your heads together! :)

asterisk_man
Feb 21, 2007, 10:55 AM
Based on the initial 4 zeros I'm led to believe that the function is f(n-1,n-2,n-3,n-4) and that terms 1 2 3 4 are the initial conditions.

Capuchin
Feb 21, 2007, 10:56 AM
You would be incorrect in that belief.

asterisk_man
Feb 21, 2007, 12:57 PM
is it a sequence which is defined by the numbers that capuchin and galactus randomly generate for the purpose of keeping asterisk_man in a perpetual state of confusion?? If that's the case, is the next term in the sequence \Phi?

Capuchin
Feb 21, 2007, 01:02 PM
Eheehehehhehe

Okay here is a huge clue.

The terms that you might want to concentrate on are five, six, eleven and twelve.

colbtech
Feb 22, 2007, 01:52 AM
Well I can't remember the last time an England opener scored 55 ? Cou;dn't you have started with a sequence like 1,2,3,4,5,

Think I could have coped with that one. (Hint: Nothing to do with cricket!)

Capuchin
Feb 22, 2007, 07:55 AM
Another clue?

The sequence is poorly defined beyond term 34

galactus
Feb 24, 2007, 02:44 PM
Cap, ol' buddy, it's time you gave it up. Think mapping and Roman numerals.

Capuchin
Feb 24, 2007, 02:52 PM
Yes I completely forgot about this lol

The sequence is formed by taking each term, removing all letters that aren't I, V, X, L, C, D, or M, and then reading the number as a roman numeral.

for example, six = ix = 9
twelve = lv = 55

It's poorly defined after term 34 because thirty-five is iiv which is not a standard roman numeral.

It is sequence A002904 (http://www.research.att.com/~njas/sequences/A002904) in the The On-Line Encyclopedia of Integer Sequences (http://www.research.att.com/~njas/sequences/).

Thanks for playing.

galactus
Feb 24, 2007, 03:29 PM
The pattern is rather obscure.

one=0
two=0
three=0
four=0
fIVe=4
sIX=9
seVen=5
eIght=1
nIne=1
ten=0
eLeVen=55
tweLVe=55
thIrteen=1
fourteen=0
fIfteen=1
sIXteen=9
seVenteen=5
eIghteen=1
nIneteen=1
twenty=0
twenty-0ne=0
twenty-two=0
twenty-three=0
twenty-four=0
twenty-fIVe=4
twenty-sIX=9
twenty-seVen=5
twenty-eIght=1
twenty-nIne=1
thIrty=1
.
.
.
.
.
seVenty-sIX=59

And so on and so on. See the pattern?

Capuchin
Feb 24, 2007, 05:11 PM
Why is vix 59? :/ it's poorly defined also. Could be 59, or 4, or 14, or 45. They would write 59 as lix

agneau
Feb 25, 2007, 02:34 AM
okay, a mini clue, it's an infinite sequence.


This reminds me of this other sequence: 3, 3, 5, 4, 4, 3, 5, 5, 4, 3, 6, 6...

(although that looks fairly regular... it is not about the numbers themselves but about the number of letters in the words ONE, TWO, THREE etc... )

I am convinced they are similar somehow... but I am thrown by the 0, 0, 0... assuming it is something to do with the words ONE, TWO etc... could it be a formula e.g. relating the number of vowels to consonants? Or should I be looking at other languages than English?

ONE, TWO, THREE all have
abs(Vowels - Consonants) - 1 = 0
but this fails with FOUR

and it could never give an answer of 9!

before I try to pursue this any further and totally go mad... am I on the right track?

a

Capuchin
Feb 25, 2007, 03:51 AM
Erm, I've given the answer ;)

agneau
Feb 25, 2007, 06:42 AM
Erm, i've given the answer ;)

LOL... I guess I should make sure I have read the whoe thread, not just the first page, before replying! At least that gave me something fun to think about for a bit. And I am relieved I wasn't being completely thick. That is the sort of sequence it is impossible to work out unless you have a BIG clue... like the answer!

Thanks

A

Capuchin
Feb 25, 2007, 07:48 AM
It's not that hard, you just need to tweak it.

asterisk_man
Feb 26, 2007, 07:45 AM
OK. I was starting to get in the right ballpark. I knew that it had something to do with the names of the numbers. Though I hadn't quite made the leap to roman numerals yet.

Tricky sequence!

asterisk_man
Feb 28, 2007, 11:10 AM
One last question. Capuchin, why is this your favorite number sequence?

Capuchin
Feb 28, 2007, 11:27 AM
Because you didn't get it.

asterisk_man
Feb 28, 2007, 11:33 AM
Oooh that's harsh. So this number sequence was your favorite because of an event that had not yet happened. (or had not yet not happened). Were you aware of this when it became your favorite? Or was there a flash of insight at the last moment? Any other insights into future events you might be able to provide us with? Next week's lotto #s perhaps? :)

Edit: send those lotto numbers in a PM if you don't mind