# \# Sequence? **URL:** \ **Category:** Factual Questions\ **Created:** [March 17, 2004, 2:20am UTC](https://boards.straightdope.com/t/sequence/234767 "2004-03-17T02:20:14Z")\ **Posts on this page:** 20\ **Page:** 1
**Author:** ![SwingWing](https://avatars.discourse-cdn.com/v4/letter/s/a3d4f5/32.png) [@SwingWing](https://boards.straightdope.com/u/SwingWing)\ **Post date:** [March 17, 2004, 2:20am UTC](https://boards.straightdope.com/t/sequence/234767/1 "2004-03-17T02:20:14Z")
4 … 15 … 10 … 9 … 16 … 12 … 13 … Next? ---
**Author:** ![BuckleberryFerry](https://avatars.discourse-cdn.com/v4/letter/b/5f9b8f/32.png) [@BuckleberryFerry](https://boards.straightdope.com/u/BuckleberryFerry)\ **Post date:** [March 17, 2004, 2:47am UTC](https://boards.straightdope.com/t/sequence/234767/2 "2004-03-17T02:47:19Z")
18? ---
**Author:** ![ftg](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/ftg/32/2801_2.png) [@ftg](https://boards.straightdope.com/u/ftg)\ **Post date:** [March 17, 2004, 3:09am UTC](https://boards.straightdope.com/t/sequence/234767/3 "2004-03-17T03:09:39Z")
Sorry, it does not appear in the [Online database of integer sequences.](http://www.research.att.com/~njas/sequences/) Chances are, just about any number can be argued as a good “next”. ---
**Author:** ![Sublight](https://avatars.discourse-cdn.com/v4/letter/s/439d5e/32.png) [@Sublight](https://boards.straightdope.com/u/Sublight)\ **Post date:** [March 17, 2004, 3:43am UTC](https://boards.straightdope.com/t/sequence/234767/4 "2004-03-17T03:43:49Z")
There’s probably some non-mathematical solution, like “words in each sentence of the Declaration of Independence” or “verses in each chapter of the Bible” or “number of times each team in the Major Leagues, starting from the northeast, has won the world series”. ---
**Author:** ![Biere](https://avatars.discourse-cdn.com/v4/letter/b/b9bd4f/32.png) [@Biere](https://boards.straightdope.com/u/Biere)\ **Post date:** [March 17, 2004, 3:51am UTC](https://boards.straightdope.com/t/sequence/234767/5 "2004-03-17T03:51:42Z")
> [@SwingWing](#): > > 4 … 15 … 10 … 9 … 16 … 12 … 13 … Next? Looks like a Mensa sequence. Any hints? … ---
**Author:** ![Mathochist](https://avatars.discourse-cdn.com/v4/letter/m/c89c15/32.png) [@Mathochist](https://boards.straightdope.com/u/Mathochist)\ **Post date:** [March 17, 2004, 5:55am UTC](https://boards.straightdope.com/t/sequence/234767/6 "2004-03-17T05:55:23Z")
> [@Biere](#): > > Looks like a Mensa sequence. Any hints? … The hint, I wager, is that this is yet another **SwingWing** thread. I propose “YASWT” as a new standard acronym. ---
**Author:** ![dnooman](https://avatars.discourse-cdn.com/v4/letter/d/839c29/32.png) [@dnooman](https://boards.straightdope.com/u/dnooman)\ **Post date:** [March 17, 2004, 6:04am UTC](https://boards.straightdope.com/t/sequence/234767/7 "2004-03-17T06:04:28Z")
I got 17. ---
**Author:** ![august9](https://avatars.discourse-cdn.com/v4/letter/a/7993a0/32.png) [@august9](https://boards.straightdope.com/u/august9)\ **Post date:** [March 17, 2004, 6:40am UTC](https://boards.straightdope.com/t/sequence/234767/8 "2004-03-17T06:40:44Z")
17 ---
**Author:** ![RayMan](https://avatars.discourse-cdn.com/v4/letter/r/e495f1/32.png) [@RayMan](https://boards.straightdope.com/u/RayMan)\ **Post date:** [March 17, 2004, 7:01am UTC](https://boards.straightdope.com/t/sequence/234767/9 "2004-03-17T07:01:24Z")
I got 193. ---
**Author:** ![pjd](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/pjd/32/3009_2.png) [@pjd](https://boards.straightdope.com/u/pjd)\ **Post date:** [March 17, 2004, 12:08pm UTC](https://boards.straightdope.com/t/sequence/234767/10 "2004-03-17T12:08:58Z")
It’s 87 I’ve seen this before. It’s a sequence of random numbers, so the next number is 46. 4 … 15 … 10 … 9 … 16 … 12 … 13 … … 275 ! Simple. ---
**Author:** ![Reuben](https://avatars.discourse-cdn.com/v4/letter/r/54ee81/32.png) [@Reuben](https://boards.straightdope.com/u/Reuben)\ **Post date:** [March 17, 2004, 12:38pm UTC](https://boards.straightdope.com/t/sequence/234767/11 "2004-03-17T12:38:51Z")
The first two pairs of entries sum to 19. The next pair sums to 18. The final number is 13, and assuming we want another pair summing to 18 my answer for the next entry is… **5**. ---
**Author:** ![jjimm](https://avatars.discourse-cdn.com/v4/letter/j/ba8739/32.png) [@jjimm](https://boards.straightdope.com/u/jjimm)\ **Post date:** [March 17, 2004, 12:45pm UTC](https://boards.straightdope.com/t/sequence/234767/12 "2004-03-17T12:45:36Z")
The differences between the numbers are as follows: +11 -5 -1 +7 -4 -1 The first pair of differences is equal to 6. The second pair of differences is equal to 6. The next pair is equal to -5. Bollocks. Hmm, OK then, add another one to that -5 to equal 6 and we have +11, so the next number is: 24 Or something. ---
**Author:** ![jimdigritz](https://avatars.discourse-cdn.com/v4/letter/j/91b2a8/32.png) [@jimdigritz](https://boards.straightdope.com/u/jimdigritz)\ **Post date:** [March 17, 2004, 12:48pm UTC](https://boards.straightdope.com/t/sequence/234767/13 "2004-03-17T12:48:31Z")
> [@pjd](#): > > It’s 87 > > I’ve seen this before. > It’s a sequence of random numbers, so the next number is 46. > > 4 … 15 … 10 … 9 … 16 … 12 … 13 … … 275 ! > > Simple. My lame take on it: **4** + **15** =19 **15** + **10** =25 **10** + **9** =19 **9** + **16** =25 **16** + **12** =25 Unfortunately the patterm seems to alter slightly and my brain is overheating trying to figure out any more… ---
**Author:** ![jimdigritz](https://avatars.discourse-cdn.com/v4/letter/j/91b2a8/32.png) [@jimdigritz](https://boards.straightdope.com/u/jimdigritz)\ **Post date:** [March 17, 2004, 12:51pm UTC](https://boards.straightdope.com/t/sequence/234767/14 "2004-03-17T12:51:43Z")
> [@jimdigritz](#): > > My lame take on it: > > **4** + **15** =19 **15** + **10** =25 **10** + **9** =19 **9** + **16** =25 **16** + **12** =25 > > Unfortunately the patterm seems to alter slightly and my brain is overheating trying to figure out any more… DOH!!! (mental note: proof post before pressing submit!!) **4** + **15** =19 **15** + **10** =25 **10** + **9** =19 **9** + **16** =25 **16** + **12** =28 **12** + **13** =25 So close to a pattern! ---
**Author:** ![Reuben](https://avatars.discourse-cdn.com/v4/letter/r/54ee81/32.png) [@Reuben](https://boards.straightdope.com/u/Reuben)\ **Post date:** [March 17, 2004, 1:11pm UTC](https://boards.straightdope.com/t/sequence/234767/15 "2004-03-17T13:11:03Z")
And now I review the OP I’ve just noticed I lost a 10 somewhere… must have hit backspace during cut’n’pasting or something… (That’s my excuse and I’m sticking to it… 🙂 ---
**Author:** ![pulykamell](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/pulykamell/32/3166_2.png) [@pulykamell](https://boards.straightdope.com/u/pulykamell)\ **Post date:** [March 17, 2004, 5:00pm UTC](https://boards.straightdope.com/t/sequence/234767/16 "2004-03-17T17:00:54Z")
I’m guessing 17, 14 I’m grouping them in threes myself: 4,15,10 9,16,12 13 It seems to better fit a pattern. The first column goes +5,+4. The second goes +1,+1. The third goes +2,+2. The difference between the last two columns is what’s added to the number in the first column. So (15-10)+4 =9 (16-12)+9 = 13. Where the 15 and 10 comes from, I don’t know, but I think it’s a valid pattern. You can extend it thusly: 4,15,10 9,16,12 13,17,14 16,18,16 18,19,18 19,20,20 But there’s probably a slightly better mathematical relationship that I’m missing on first glance. Still, I think 17 followed by 14 is a good answer. ---
**Author:** ![SwingWing](https://avatars.discourse-cdn.com/v4/letter/s/a3d4f5/32.png) [@SwingWing](https://boards.straightdope.com/u/SwingWing)\ **Post date:** [March 17, 2004, 8:28pm UTC](https://boards.straightdope.com/t/sequence/234767/17 "2004-03-17T20:28:31Z")
> [@Mathochist](#): > > The hint, I wager, is that this is yet another **SwingWing** thread. I propose “YASWT” as a new standard acronym. Don’t know about “YASWT?” The only hint was that a portion of the sequence becomes repetitive. ---
**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\ **Post date:** [March 17, 2004, 9:13pm UTC](https://boards.straightdope.com/t/sequence/234767/18 "2004-03-17T21:13:12Z")
The 5th differences are not constant, so if this is generated by a polynomial, its degree is at least 6. ---
**Author:** ![aerodave](https://avatars.discourse-cdn.com/v4/letter/a/f08c70/32.png) [@aerodave](https://boards.straightdope.com/u/aerodave)\ **Post date:** [March 17, 2004, 9:41pm UTC](https://boards.straightdope.com/t/sequence/234767/19 "2004-03-17T21:41:14Z")
> [@ultrafilter](#): > > The 5th differences are not constant, so if this is generated by a polynomial, its degree is at least 6. This is intriguing. Could you fill me in on this bit of mathematical knowledge with which I am obviously unaware? ---
**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\ **Post date:** [March 17, 2004, 9:56pm UTC](https://boards.straightdope.com/t/sequence/234767/20 "2004-03-17T21:56:41Z")
> [@audilover](#): > > This is intriguing. Could you fill me in on this bit of mathematical knowledge with which I am obviously unaware? [symbol]D[/symbol][sub]h[/sub] is the finite difference operator, with [symbol]D[/symbol][sub]h[/sub]f = f(x + h) - f(x). [symbol]D[/symbol][sub]h[/sub][sup]n[/sup] is defined by [symbol]D[/symbol][sub]h[/sub][sup]1[/sup]f = [symbol]D[/symbol][sub]h[/sub]f, and [symbol]D[/symbol][sub]h[/sub][sup]n+1[/sup]f = [symbol]D[/symbol][sub]h[/sub][symbol]D[/symbol][sub]h[/sub][sup]n[/sup]f. We also define [symbol]D[/symbol][sub]h[/sub][sup]0[/sup]f = f. It’s relatively straightforward to show that [symbol]D[/symbol][sub]h[/sub][sup]n[/sup]x[sup]n[/sup] is constant, and [symbol]D[/symbol][sub]h[/sub][sup]k[/sup]x[sup]n[/sup] = 0 whenever k \> n, although the details can get messy. It’s also easy to show that [symbol]D[/symbol][sub]h[/sub][sup]n[/sup]([symbol]a[/symbol]f + [symbol]b[/symbol]g) = [symbol]aD[/symbol][sub]h[/sub][sup]n[/sup]f + [symbol]bD[/symbol][sub]h[/sub][sup]n[/sup]g. From this, it’s easy to show that [symbol]D[/symbol][sub]h[/sub][sup]degree§[/sup]p is constant for any polynomial function p. [Next page](https://boards.straightdope.com/t/sequence/234767.md?page=2)