Ducky Havok Posted June 10, 2005 Share Posted June 10, 2005 Find the next number and explain the pattern: 14,22,44,74,158,? Good luck! Link to comment Share on other sites More sharing options...
Peppers Posted June 13, 2005 Share Posted June 13, 2005 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! Link to comment Share on other sites More sharing options...
gnpatterson Posted June 15, 2005 Share Posted June 15, 2005 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. Link to comment Share on other sites More sharing options...
Ducky Havok Posted June 15, 2005 Author Share Posted June 15, 2005 no, it's purely mathematical Link to comment Share on other sites More sharing options...
gnpatterson Posted June 16, 2005 Share Posted June 16, 2005 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? Link to comment Share on other sites More sharing options...
gnpatterson Posted June 16, 2005 Share Posted June 16, 2005 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. Link to comment Share on other sites More sharing options...
gnpatterson Posted June 16, 2005 Share Posted June 16, 2005 Got IT! by cheating of course would the next be 212? Link to comment Share on other sites More sharing options...
Ducky Havok Posted June 16, 2005 Author Share Posted June 16, 2005 Yup, you got it, how'd you cheat though? I thought you said that site didn't work? Link to comment Share on other sites More sharing options...
Martin Posted June 17, 2005 Share Posted June 17, 2005 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. Link to comment Share on other sites More sharing options...
Ducky Havok Posted June 17, 2005 Author Share Posted June 17, 2005 Nope Martin, not it Link to comment Share on other sites More sharing options...
Martin Posted June 17, 2005 Share Posted June 17, 2005 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? Link to comment Share on other sites More sharing options...
gnpatterson Posted June 17, 2005 Share Posted June 17, 2005 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 Link to comment Share on other sites More sharing options...
Ducky Havok Posted June 17, 2005 Author Share Posted June 17, 2005 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. Link to comment Share on other sites More sharing options...
Martin Posted June 17, 2005 Share Posted June 17, 2005 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. Link to comment Share on other sites More sharing options...
Ducky Havok Posted June 17, 2005 Author Share Posted June 17, 2005 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. Link to comment Share on other sites More sharing options...
gnpatterson Posted June 18, 2005 Share Posted June 18, 2005 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 Link to comment Share on other sites More sharing options...
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