[Guest]

4, 10, 24, 32, 45, 54, 84, 104, 117, 130...

What's next?

and another related one:

4, 8, 18, 20, 25, 24, 42, 48, 45, 40...

Edited June 17, 2008 by engspangussian

[Guest]

like most, I am certain the 1st multiplier is 11 (+1 numerical sequence).

The second multiplier is a bit trickier. The only precidence set is +0, +1, and +3. I don't really see a pattern there (1, 3, 0, 1, 0, 3, 1, 0, 0, ??)

[Guest]

after looking at Jarod's, I have come up with:

154 for the first pattern and 44 for the second pattern. I know you have said 154 is wrong in the past but I really feel confident with the reasoning here.

The difference between the two patterns should be 110 for the next 2 numbers right?

[Guest]

ar the next numbers 44, 72, 65

[Guest]

ar the next numbers 44, 72, 65

I agree

I think the next 3 numbers for the 1st pattern are

154, 204, and 221

while the next 3 numbers for the second pattern are

44, 72, and 65 (like Vimil posted earlier)

[Guest]

are the next numbers 140, 225, 240

[Guest]

are the next numbers 176, 192 221

Edited June 17, 2008 by vimil

[Guest]

none correct so far, so I think I need to post some hints.

everyone is using the same (or similar) method to look for the pattern. Pattern doesn't mean you're adding the same thing every time. The pattern here is that every term is derived in a similar way. It is a list.

I included 2 different sequences so that you could see similarities to find the pattern. However, they are separate sequences with separate answers. I'm looking for the next term for the first one, AND the next term for the second, as well as how both lists are derived.

if these two don't help, there'll be a bigger one later.

[Guest]

none correct so far, so I think I need to post some hints.

everyone is using the same (or similar) method to look for the pattern. Pattern doesn't mean you're adding the same thing every time. The pattern here is that every term is derived in a similar way. It is a list.

I included 2 different sequences so that you could see similarities to find the pattern. However, they are separate sequences with separate answers. I'm looking for the next term for the first one, AND the next term for the second, as well as how both lists are derived.

if these two don't help, there'll be a bigger one later.

This is how I came up with ths solution for the 2nd sequence.

from bigwilly's post the second sequence can be written as follows

4, 8, 18, 20, 25, 24, 42, 48, 45, 40...

4*1, 4*2, 6*3, 5*4, 5*5, 4*6, 6*7, 6*8, 5*9, 4*10, ...

looking at the first factor of each term, we have this sequence

4, 4, 6, 5, 5, 4, 6, 6, 5, 4

and this sequence looks like its obtained by rotating the pattern 5 4 6

(4, 6, 5), (5,4,6), (6, 5, 4)

so the next rotation should give (4, 6, 5)

so next terms should be 4*11, 6*12, 5*13

which is 44, 72, 65

[Guest]

This is how I came up with ths solution for the 2nd sequence.

from bigwilly's post the second sequence can be written as follows

4, 8, 18, 20, 25, 24, 42, 48, 45, 40...

4*1, 4*2, 6*3, 5*4, 5*5, 4*6, 6*7, 6*8, 5*9, 4*10, ...

looking at the first factor of each term, we have this sequence

4, 4, 6, 5, 5, 4, 6, 6, 5, 4

and this sequence looks like its obtained by rotating the pattern 5 4 6

(4, 6, 5), (5,4,6), (6, 5, 4)

so the next rotation should give (4, 6, 5)

so next terms should be 4*11, 6*12, 5*13

which is 44, 72, 65

interesting reasoning, but it's not a rotation of a pattern.

each term is derived individually. the pattern is the method by which each term is derived. term (n+1) is not dependent on the value of term n.

[Yoruichi-san]

I think I got the second pattern:

...77,84,117

[Yoruichi-san]

I think I got the second pattern:

...77,84,117

Oh, and this is the pattern:

a(n)=n*(number of letters in the word for "n"+1)

i.e. O-N-E and T-W-O both have 3 letters, so the second multiplier is 3+1=4. T-H-R-E-E has 5 letters, so the second multiplier is 5+1=6.

E-L-E-V-E-N and T-W-E-L-V-E both have 6 letters, so the eleventh and twelfth numbers in the sequence should be 11*(6+1)=77 and 12*(6+1)=84. T-H-I-R-T-E-E-N has 8 letters, so the thirteenth number should be 13*(8+1)=117.

[Yoruichi-san]

Oh, and after figuring that out, I get the first one too...

187,216,273

[Yoruichi-san]

Oh, and after figuring that out, I get the first one too...

187,216,273

Right, I forgot to include the pattern again, so here it is

a(n)=n*(number of letters in the word for "n"+n)

I.E. The second multipliers for: ONE is 3+1=4

TWO is 3+2=5

THREE is 5+3=8

FOUR is 4+4=8

FIVE is 4+5=9

SIX is 3+6=9

SEVEN is 5+7=12

EIGHT is 5+8=13

NINE is 4+9=13

TEN is 3+10=13

so the next ones should be:

ELEVEN is 6+11=17

TWELVE is 6+12=18

THIRTEEN is 8+13=21

So for n=11,12,13, a(n) should be 11*17=187,12*18=216, 13*21=273

[akaslickster]

Right, I forgot to include the pattern again, so here it is

a(n)=n*(number of letters in the word for "n"+n)

I.E. The second multipliers for: ONE is 3+1=4

TWO is 3+2=5

THREE is 5+3=8

FOUR is 4+4=8

FIVE is 4+5=9

SIX is 3+6=9

SEVEN is 5+7=12

EIGHT is 5+8=13

NINE is 4+9=13

TEN is 3+10=13

so the next ones should be:

ELEVEN is 6+11=17

TWELVE is 6+12=18

THIRTEEN is 8+13=21

So for n=11,12,13, a(n) should be 11*17=187,12*18=216, 13*21=273

You seem to have a good answer, I put my chips here.

[Guest]

A counting type solution based on letters was going to be my second approach. GJ Yoruichi-San

[Guest]

A counting type solution based on letters was going to be my second approach. GJ Yoruichi-San

Crap, I remember a quote that has something to do with genius and how they think that relates.

It takes immense genius to represent, simply and sincerely, what we see right in front of us.

--Edmond Duranty

Nice answer.

[Guest]

Right, I forgot to include the pattern again, so here it is

a(n)=n*(number of letters in the word for "n"+n)

I.E. The second multipliers for: ONE is 3+1=4

TWO is 3+2=5

THREE is 5+3=8

FOUR is 4+4=8

FIVE is 4+5=9

SIX is 3+6=9

SEVEN is 5+7=12

EIGHT is 5+8=13

NINE is 4+9=13

TEN is 3+10=13

so the next ones should be:

ELEVEN is 6+11=17

TWELVE is 6+12=18

THIRTEEN is 8+13=21

So for n=11,12,13, a(n) should be 11*17=187,12*18=216, 13*21=273

Wow, good stuff!!

[Guest]

4, 10, 24, 32, 45, 54, 84, 104, 117, 130...

What's next?

and another related one:

4, 8, 18, 20, 25, 24, 42, 48, 45, 40...

Are we allowed to know if the series are finite?

[Yoruichi-san]

It takes immense genius to represent, simply and sincerely, what we see right in front of us.

--Edmond Duranty

Well, that's what differential equations are for (and why I say that they are the only useful form of math).

You can always write a differential equation describing what we observe. Solving that differential equation is another matter though...

Thanks a lot for the words of praise!

[Yoruichi-san]

Well, that's what differential equations are for (and why I say that they are the only useful form of math).

You can always write a differential equation describing what we observe. Solving that differential equation is another matter though...

Thanks a lot for the words of praise!

Oh, and thanks to engspangussian for the clever pattern...and the people who figured out the multiplying thing! This was totally a team effort, which is why I like this forum!

[Guest]

Yes, Yoruichi-san got it! Good job!!

There is another way to describe pattern #2, the way I thought initially, which makes it even more similar to the other (although probably not as simple as Yoruichi-san's formula):

pattern 1- (n + number of letters in n) * n

pattern 2- (n * number of letters in n) + n

And this is the pattern I based these off of:

4, 5, 8, 8, 9, 9, 12, 13, 13, 13

and the formula is :

n + number of letters in n

To everyone else, great ideas and great job on the collaboration. I agree, that is one of the coolest things about this site.