# Next in series 1,4,2,8,2,16,... **URL:** \ **Category:** Miscellaneous and Personal Stuff I Must Share\ **Created:** [June 26, 2014, 5:46pm UTC](https://boards.straightdope.com/t/next-in-series-1-4-2-8-2-16/691713 "2014-06-26T17:46:15Z")\ **Posts on this page:** 20\ **Page:** 1
**Author:** ![Greg\_Charles](https://avatars.discourse-cdn.com/v4/letter/g/839c29/32.png) [@Greg\_Charles](https://boards.straightdope.com/u/Greg_Charles)\ **Post date:** [June 26, 2014, 5:46pm UTC](https://boards.straightdope.com/t/next-in-series-1-4-2-8-2-16/691713/1 "2014-06-26T17:46:15Z")
A coworker brought in this problem his daughter had been given in her eighth grade math class. The challenge is to find the next three elements, and we’re all baffled. Personally, I think someone has screwed up the numbers. If the SDMB can’t get it, I’ll know I’m right. ---
**Author:** ![SylverOne](https://avatars.discourse-cdn.com/v4/letter/s/c0e974/32.png) [@SylverOne](https://boards.straightdope.com/u/SylverOne)\ **Post date:** [June 26, 2014, 5:57pm UTC](https://boards.straightdope.com/t/next-in-series-1-4-2-8-2-16/691713/2 "2014-06-26T17:57:46Z")
2,32,2,64,2,128 no idea… ---
**Author:** ![Sahirrnee](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/sahirrnee/32/13937_2.png) [@Sahirrnee](https://boards.straightdope.com/u/Sahirrnee)\ **Post date:** [June 26, 2014, 6:04pm UTC](https://boards.straightdope.com/t/next-in-series-1-4-2-8-2-16/691713/3 "2014-06-26T18:04:17Z")
1,4,2,8,2,16,3,32,3,64,3,128,4,256,4,…? ---
**Author:** ![Greg\_Charles](https://avatars.discourse-cdn.com/v4/letter/g/839c29/32.png) [@Greg\_Charles](https://boards.straightdope.com/u/Greg_Charles)\ **Post date:** [June 26, 2014, 6:12pm UTC](https://boards.straightdope.com/t/next-in-series-1-4-2-8-2-16/691713/4 "2014-06-26T18:12:15Z")
> [@SylverOne](#): > > 2,32,2,64,2,128 no idea… Yeah, that’s the best I came up with too. If it were 2,4,2,8,2,16… then that would make sense, but starting with 1? I don’t think so. > [@Sahirrnee](#): > > 1,4,2,8,2,16,3,32,3,64,3,128,4,256,4,…? I’m not following that. Can you explain your reasoning? ---
**Author:** ![Kobalt](https://avatars.discourse-cdn.com/v4/letter/k/41988e/32.png) [@Kobalt](https://boards.straightdope.com/u/Kobalt)\ **Post date:** [June 26, 2014, 6:16pm UTC](https://boards.straightdope.com/t/next-in-series-1-4-2-8-2-16/691713/5 "2014-06-26T18:16:38Z")
1,4,2,8,2,16,4,32,4,64,8,128 or one-fourth,one-fourth, one-eighth, one-eighth, one-sixteenth, one-sixteenth, and so on ---
**Author:** ![Tapioca\_Dextrin](https://avatars.discourse-cdn.com/v4/letter/t/3d9bf3/32.png) [@Tapioca\_Dextrin](https://boards.straightdope.com/u/Tapioca_Dextrin)\ **Post date:** [June 26, 2014, 6:17pm UTC](https://boards.straightdope.com/t/next-in-series-1-4-2-8-2-16/691713/6 "2014-06-26T18:17:23Z")
There is one 1, two 2s, three 3s etc. - shuffled into the powers of 2 It would logically consistent, but not correct in any mathematical sense ---
**Author:** ![mhendo](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/mhendo/32/3159_2.png) [@mhendo](https://boards.straightdope.com/u/mhendo)\ **Post date:** [June 26, 2014, 6:33pm UTC](https://boards.straightdope.com/t/next-in-series-1-4-2-8-2-16/691713/7 "2014-06-26T18:33:17Z")
> [@Sahirrnee](#): > > 1,4,2,8,2,16,3,32,3,64,3,128,4,256,4,…? This is what i came up with, but i think it’s a stupid question. And it’s not really a math question at all. ---
**Author:** ![jackdavinci](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/jackdavinci/32/3259_2.png) [@jackdavinci](https://boards.straightdope.com/u/jackdavinci)\ **Post date:** [June 26, 2014, 6:38pm UTC](https://boards.straightdope.com/t/next-in-series-1-4-2-8-2-16/691713/8 "2014-06-26T18:38:39Z")
It’s not cataloged as a well known integer series: [1,4,2,8,2,16 - OEIS](https://oeis.org/search?q=1%2C4%2C2%2C8%2C2%2C16&language=english&go=Search) ---
**Author:** ![Giles](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/giles/32/60_2.png) [@Giles](https://boards.straightdope.com/u/Giles)\ **Post date:** [June 26, 2014, 6:41pm UTC](https://boards.straightdope.com/t/next-in-series-1-4-2-8-2-16/691713/9 "2014-06-26T18:41:16Z")
Assuming the series is limited to powers of 2, a equivalent series would be the exponents: 0, 2, 1, 3, 1, 4, … What’s the rule there? ---
**Author:** ![SylverOne](https://avatars.discourse-cdn.com/v4/letter/s/c0e974/32.png) [@SylverOne](https://boards.straightdope.com/u/SylverOne)\ **Post date:** [June 26, 2014, 6:43pm UTC](https://boards.straightdope.com/t/next-in-series-1-4-2-8-2-16/691713/10 "2014-06-26T18:43:02Z")
> [@Sahirrnee](#): > > 1,4,2,8,2,16,3,32,3,64,3,128,4,256,4,…? That makes sense to me. I just wasn’t getting the 1 and 2’s, but that solution works. ---
**Author:** ![bup](https://avatars.discourse-cdn.com/v4/letter/b/6bbea6/32.png) [@bup](https://boards.straightdope.com/u/bup)\ **Post date:** [June 26, 2014, 6:52pm UTC](https://boards.straightdope.com/t/next-in-series-1-4-2-8-2-16/691713/11 "2014-06-26T18:52:35Z")
A valid answer that the teacher will probably call wrong is 1,4,2,8,2,16 again. So the next three elements would be 1,4,2. But I like **Sahirnee** ’s answer. ---
**Author:** ![Sahirrnee](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/sahirrnee/32/13937_2.png) [@Sahirrnee](https://boards.straightdope.com/u/Sahirrnee)\ **Post date:** [June 26, 2014, 6:54pm UTC](https://boards.straightdope.com/t/next-in-series-1-4-2-8-2-16/691713/12 "2014-06-26T18:54:03Z")
> [@Greg\_Charles](#): > > Yeah, that’s the best I came up with too. If it were 2,4,2,8,2,16… then that would make sense, but starting with 1? I don’t think so. > > I’m not following that. Can you explain your reasoning? There is 1 1, 2 2s, 3 3s, and so on Sometimes in number patterns the pattern skips over numbers so that every other number follows a pattern, or every third number follows a pattern. so this pattern could be 1,4,2,8,2,16,3,32,3,64,3,128,4 ---
**Author:** ![Giles](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/giles/32/60_2.png) [@Giles](https://boards.straightdope.com/u/Giles)\ **Post date:** [June 26, 2014, 7:51pm UTC](https://boards.straightdope.com/t/next-in-series-1-4-2-8-2-16/691713/13 "2014-06-26T19:51:00Z")
I don’t think it’s obvious what the next item in the series 1, 2, 2, … is. The series could be: 1, 2, 2, 3, 2, 4, 2, 4, 3, 4, 2, 5, … (That’s the number of factors, including itself and 1, of each of the natural numbers: 1 factor of 1, 2 factors of both 2 and 3, 3 factors of 4, etc.) ---
**Author:** ![Sahirrnee](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/sahirrnee/32/13937_2.png) [@Sahirrnee](https://boards.straightdope.com/u/Sahirrnee)\ **Post date:** [June 26, 2014, 10:17pm UTC](https://boards.straightdope.com/t/next-in-series-1-4-2-8-2-16/691713/14 "2014-06-26T22:17:01Z")
That’s a problem with number sequences, quite often there are more than one correct answer. Everybody’s brain works differently and what jumps out at one person isn’t apparent to another. I don’t know that my answer is right but it’s the direction my brain took. ---
**Author:** ![Revtim](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/revtim/32/1042_2.png) [@Revtim](https://boards.straightdope.com/u/Revtim)\ **Post date:** [June 27, 2014, 12:35am UTC](https://boards.straightdope.com/t/next-in-series-1-4-2-8-2-16/691713/15 "2014-06-27T00:35:00Z")
> [@Sahirrnee](#): > > That’s a problem with number sequences, quite often there are more than one correct answer. > Everybody’s brain works differently and what jumps out at one person isn’t apparent to another. > > I don’t know that my answer is right but it’s the direction my brain took. Your answer is right, it just may not be the one right answer the author of the sequence is looking for. ---
**Author:** ![Sage\_Rat](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/sage_rat/32/399_2.png) [@Sage\_Rat](https://boards.straightdope.com/u/Sage_Rat)\ **Post date:** [June 27, 2014, 12:39am UTC](https://boards.straightdope.com/t/next-in-series-1-4-2-8-2-16/691713/16 "2014-06-27T00:39:39Z")
The current sequence, from bit shifting perspective is: \<\< 2 \>\> 1 \<\< 2 \>\> 2 \<\< 3 So one possible continuation would be: ``` >> 3 ``` \<\< 3 \>\> 4 That would make the full pattern: 1,4,2,8,2,16,2,16,1 ---
**Author:** ![yarblek](https://avatars.discourse-cdn.com/v4/letter/y/71e660/32.png) [@yarblek](https://boards.straightdope.com/u/yarblek)\ **Post date:** [June 27, 2014, 12:44am UTC](https://boards.straightdope.com/t/next-in-series-1-4-2-8-2-16/691713/17 "2014-06-27T00:44:53Z")
Why can’t this be the pattern? 1,4,2,8,2,16,1,32,2,64,2,128,1,256… 😛 ---
**Author:** ![Kimble](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/kimble/32/19185_2.png) [@Kimble](https://boards.straightdope.com/u/Kimble)\ **Post date:** [June 27, 2014, 1:12am UTC](https://boards.straightdope.com/t/next-in-series-1-4-2-8-2-16/691713/18 "2014-06-27T01:12:42Z")
My arbitrary (yet correct) answer: f(1) = 1 f(2) = 4 If x is odd, f(x) = f(x-2) / ( 2\*f(x-1) ) If x is even, f(x) = f(x-2) \* f(x-1) Therefore: f(3) = 2 f(4) = 8 f(5) = 2 f(6) = 16 f(7) = **4** f(8) = **64** f(9) = **8** f(10) = 512 f(11) = 32 f(12) = 16384 f(13) = 256 f(14) = 4194304 etc. If forced to guess, though, I would expect a typo and the actual question would be 1, 4, 2, 8, 3, 16. ---
**Author:** ![bup](https://avatars.discourse-cdn.com/v4/letter/b/6bbea6/32.png) [@bup](https://boards.straightdope.com/u/bup)\ **Post date:** [June 27, 2014, 1:46am UTC](https://boards.straightdope.com/t/next-in-series-1-4-2-8-2-16/691713/19 "2014-06-27T01:46:45Z")
The problem with number sequence problems is how damned smug the person who creates the question is. Thinks s/he’s so great. Let me tell you something, number sequence maker-upper: you’re not great at all. You suck. ---
**Author:** ![Dead\_Cat](https://avatars.discourse-cdn.com/v4/letter/d/9fc29f/32.png) [@Dead\_Cat](https://boards.straightdope.com/u/Dead_Cat)\ **Post date:** [June 27, 2014, 12:23pm UTC](https://boards.straightdope.com/t/next-in-series-1-4-2-8-2-16/691713/20 "2014-06-27T12:23:32Z")
> [@Giles](#): > > I don’t think it’s obvious what the next item in the series > 1, 2, 2, … > is. You’re right, it isn’t obvious - it could equally be 1, 2, 2, 2, 3, 2, 4, 2, 5, 2, 6, 2… - a sequence that will probably be familiar to anyone who has played in an orchestra, especially brass or percussion! > [@bup](#): > > The problem with number sequence problems is how damned smug the person who creates the question is. Thinks s/he’s so great. Let me tell you something, number sequence maker-upper: you’re not great at all. You suck. Ha! I agree that the most likely answer in this case is a typo. The student’s best bet might be to give one (or more) of the answers in this thread and add the possibility of the typo, for which a nice teacher might give extra credit. A nasty teacher might mark it as wrong and just give the arbitrary answer the question-setter has decided on. [Next page](https://boards.straightdope.com/t/next-in-series-1-4-2-8-2-16/691713.md?page=2)