Numbers!

[Ducky Havok]

Find the next number and explain the pattern:

 

14,22,44,74,158,?

 

Good luck!

[Peppers]

No idea... i found a simple pattern for the first 4 numbers ((sum of last 2 numbers) + 8) but that 158 is laughing at me!

[gnpatterson]

Can you assure us it is mathematical? is it perhaps cultural or historical like the ages of the pharohs in the second era or the spacing in days between British bank holidays.

[Ducky Havok]

no, it's purely mathematical

[gnpatterson]

thanks then I'll assume it is something combinatorial

 

and it has a plane of symmetry (or some sort of reflection) because all the number are even

 

Am I warm?

[gnpatterson]

I gave up looking for myself and decided to cheat. I used

 

http://www.research.att.com/~njas/sequences/ (the on-line dictionary of integer sequences)

 

but even it could not "get" it!! This must be pretty hard so I admit defeat, go on tell us the answer, please.

[gnpatterson]

Got IT!

 

by cheating of course would the next be 212?

[Ducky Havok]

Yup, you got it, how'd you cheat though? I thought you said that site didn't work?

[Martin]

Yup, you got it, how'd you cheat though? I thought you said that site didn't work?

 

I don't understand the sequence yet but have glimmering that the next one after 212 could be 274.

please let me know if that is right.

[Ducky Havok]

Nope Martin, not it

[Martin]

Nope Martin, not it

 

well I salute Patterson for getting it.

 

devilish elusive sequence. perhaps you could say what IS the correct next term after 212?

 

or would you wish to put it out as a general question and see if Patterson replies?

[gnpatterson]

by cheating I mean I resorted to using google and excel

 

I decided i didnt know enough and went to mathworld to learn about the mcnugget numbers and realised that I could learn it all quickly enough so I did a site search for some of the numbers and found the sequence that this sequence is based on. Spotting how it was modified was easy as I had already been trying a zillion sequences that used this as a key.

 

PS I think the next is 344 but will tell you that 274 was almost a prime candidate for being the next one

[Ducky Havok]

I didn't know this was based on a sequence actually, I just made it up in my head. 344 is right, might as well just say the pattern now gnpatterson.

[Martin]

I didn't know this was based on a sequence actually, I just made it up in my head.

 

congratulations on making up a non-obvious pattern that turns out to have been in the expert's books already. I never heard of "mcnugget numbers".

 

344 is right, might as well just say the pattern now gnpatterson.

yeah, might as well. i, for one, am not going to guess it, and am curious how the sequence works.

[Ducky Havok]

I just looked up what a McNugget number is... I can't actually believe that this is a mathematical term, found on wolfram nonetheless.

 

McNugget Numbers

 

... I don't see how this had anything to do with my sequence though. Mine was: (prime number+2)^2-prime number

 

Please explain how you got that from McNugget Numbers gnpatterson.

[gnpatterson]

sorry for misleading you (not intentional)

 

what I meant was that when I started to do the "forwards" research to solve the puzzle I started to learn about the existing number including the mcnugget numbers.

 

I started with the Catalan numbers then

 

I came across the the page of "Miscellaneous Special Numbers"

 

http://mathworld.wolfram.com/topics/MiscellaneousSpecialNumbers.html

 

hence the McNugget Numbers

 

eventually I found the key to your sequence

 

http://mathworld.wolfram.com/PlaneDivisionbyCircles.html

 

I realalised straight away that the gap was due to the selection of prime numbers as the base of the sequence.

 

It would been neater if you had made it that the number of circles was prime.

 

It is thus really just coincidence/chance that I found the answer.

 

The mcnugget numbers were a bonus of the journey I felt worth reporting