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#1 2005-08-04 01:30:23

master
Member
Registered: 2005-08-04
Posts: 23

sequence

I got this problem with no answers.
somebody please help me. it goes like this:

What is the next number in this sequence: 1, 2, 5, 12, 1, 13, 30, 49, 1127, 1156, 1125?

help
thanx

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#2 2005-08-04 05:00:59

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

Re: sequence

The graphing function in Excel says that the sequence doesn't have a pattern in a polynomial of an order less than 7, and it's not a linear, power or exponential function. It is possible to create a pattern to fit the sequence, but it will probably involve x^10 and be very horrible in general. The next number in the sequence would probably be a fraction as well. I can't see any obvious pattern, so I think it's probably got some obscure non-mathematical reasoning behind it. If you tell us where you got the puzzle from, we might be able to help more.


Why did the vector cross the road?
It wanted to be normal.

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#3 2005-08-04 06:31:13

master
Member
Registered: 2005-08-04
Posts: 23

Re: sequence

it's from a contest  online. what i posted previously was all that was to the question. the sequence looks kind of odd, so i reckon there is a "semi-mathematical" sequence behind it. do you have any suggestions what the next number can be, just any random suggestion?

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#4 2005-08-04 11:11:08

master
Member
Registered: 2005-08-04
Posts: 23

Re: sequence

i see what you mean. still having some ideas are better then nothing right?

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#5 2005-08-04 11:32:35

MathsIsFun
Administrator
Registered: 2005-01-21
Posts: 7,711

Re: sequence

Another thought (not follwed up):

1, 2, 5, 12,
1, 13, 30, 49,
1127, 1156, 1125, ????


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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#6 2005-08-04 12:06:44

master
Member
Registered: 2005-08-04
Posts: 23

Re: sequence

i kind of thought about that, but the first two lists they just increase all the way, and the last one decrease to 1125 from 1156. another mystery.

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#7 2005-08-04 23:32:27

wcy
Member
Registered: 2005-08-04
Posts: 117

Re: sequence

the fifth term is really weird (1) and last term
cos other than the fifth and last term, the sequence is generally increasing

there are also a few perfect squares hidden in the sequence, eg
1, 25, 121, 49, 1156

Last edited by wcy (2005-08-04 23:43:38)

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#8 2005-08-04 23:46:19

Robin
Guest

Re: sequence

hi,

New to the forum and thought I'd add my 1pence worth.

I have been unable to find the most likely number that is required, but with sequences, there generally isnt only a single no. that is correct. Any number can be written as the next and even proof provided for it being there.

A good way of identifying sequences is to use finite differences. I at first tried this method and it failed to provide a concrete algo, *but* it did show me a pattern.

I haven't had my daily intake of coffee, so forgive any errors (Like spotting the obvious)

Finite differences work on apply subsequent differences between no.s .. Im only interested in the first interation for my example.

1,  2,  5,  12,    1,    13,    30,     49,       1127,     1156,     1125   (Original)
   1   3   7    -11   12     17     19      1078        29         -31          (Difference)

Ok notice that the difference gives the answer to the next no.
Starting difference 1+2=3 +2=5+7=12+-11 = 1 etc

Now I havent looked properly, there may be a hidden pattern in the difference which points to the desired next difference (Need Coffee) but the answer can be any no.

Lets say the next sequence is 1094. This would make the difference -31.
so 1125 + -31 = 1094

Anyway, thats my thoughts, good luck and pls take a look at my post I need your help.

Robin

#9 2005-08-05 00:06:53

Jai Ganesh
Administrator
Registered: 2005-06-28
Posts: 45,956

Re: sequence

Good post, and Welcome, Robin!
Subsequent differences, yes, sometimes they do help in find the next number in sequences.
But, what you have pointed out is, I feel, not acceptable.
You have found the difference, and then added that to the previous term.
In mathematical terms, you have found the difference between 2 terms, a and b, then added the difference to a, which would have to be b!


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#10 2005-08-05 00:13:16

wcy
Member
Registered: 2005-08-04
Posts: 117

Re: sequence

1, 2, 5, 12, 1, 13, 30, 49, 1127, 1156, 1125?
i found this pattern:
split the numbers into groups of 3, and multiply their digits together

1
2
5  (1+2²=5)

1x2=2
1
1x3=3 (2+1²=3)

3*0=0
4x9=36, 3x6=18, 1x8=8
1*1*2*7=14, 1*4=4  (0+8²=64=4(take last digit))

1*1*5*6=30, 3*0=0
1*1*2*5=10, 1*0=0
0+0²=0
hence the answer can be any 4 digit number whose digits multiply to 0 eg. 1110.

that is the only pattern i managed to find..
but i suspect that it is significant for 1156 to be a perfect square

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#11 2005-08-05 13:11:45

master
Member
Registered: 2005-08-04
Posts: 23

Re: sequence

hmm... nice wcy. i m pretty sure that the pattern you found is no coincidence. im now looking deeper through the hints you gave me. there must be more factors to determine the next number....

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#12 2005-08-05 13:16:14

master
Member
Registered: 2005-08-04
Posts: 23

Re: sequence

www.mathwizz.com
but you need a user id and pass word you can use mine

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#13 2005-08-05 13:22:11

master
Member
Registered: 2005-08-04
Posts: 23

Re: sequence

oh ok

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#14 2005-08-05 13:25:16

master
Member
Registered: 2005-08-04
Posts: 23

Re: sequence

i'm not sure if its a coincidence, but look what i just found:
the last 2 numbers of sequence is "1156, 1125" add their first 2 values, or ones, gives us 256 and 225, which turns out to be both perfect square, and in order: they are 14,15 (14^2, 15^2)

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#15 2005-08-05 13:31:27

master
Member
Registered: 2005-08-04
Posts: 23

Re: sequence

I Mean 16,15 Sorry

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#16 2005-08-05 13:39:43

master
Member
Registered: 2005-08-04
Posts: 23

Re: sequence

i dont know it was just for fun sortof
i was looking at the numbers and was adding stuff and found it. i didnt expect it to work

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#17 2005-08-05 14:05:22

master
Member
Registered: 2005-08-04
Posts: 23

Re: sequence

very reasonable if you ask me but apparently not

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#18 2005-08-06 01:18:36

master
Member
Registered: 2005-08-04
Posts: 23

Re: sequence

yeah thats waht i think

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#19 2005-08-06 01:26:43

master
Member
Registered: 2005-08-04
Posts: 23

Re: sequence

yeah, and it doesnt work

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#20 2005-08-06 01:39:10

master
Member
Registered: 2005-08-04
Posts: 23

Re: sequence

not really usually senior question are easier this one just ... dunno lack information or something. for instance, the code you found yesterday is perfectly reasonable

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#21 2005-08-06 01:52:08

master
Member
Registered: 2005-08-04
Posts: 23

Re: sequence

i know what you mean

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#22 2005-08-06 04:27:16

master
Member
Registered: 2005-08-04
Posts: 23

Re: sequence

yes, they post it tomorrow

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#23 2005-08-06 04:28:21

master
Member
Registered: 2005-08-04
Posts: 23

Re: sequence

im trying to solve it before that
do you have msn IM?
we could discuss

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#24 2005-08-06 04:35:09

master
Member
Registered: 2005-08-04
Posts: 23

Re: sequence

yup

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#25 2005-08-06 18:56:46

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

Re: sequence

Two little nuggets of knowledge for anyone who's interested.

1) The contest is over, so unless kylekatarn and master got IM'ing and didn't come back here, they're too late.
2) The website has a little thing called the 'rerun contest', where it chooses a random puzzle from its archive and lets you solve it for points, for people like me who come in halfway through a contest to help them catch up. That means that the answer could still be valuable to puzzlers even once the contest is over. For this reason, NO ANSWER PROVIDED. big_smile

The bonus question is, unfortunately, lost forever...


Why did the vector cross the road?
It wanted to be normal.

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