Timeline for Surprising behaviour of polynomial that generates the series 1,2,4,8,...2^(k-1)
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| S Jul 26, 2017 at 10:04 | history | suggested | Glorfindel | CC BY-SA 3.0 |
formatting, thanks removed as per https://meta.stackexchange.com/q/2950/295232
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| Jul 26, 2017 at 9:47 | review | Suggested edits | |||
| S Jul 26, 2017 at 10:04 | |||||
| Oct 16, 2010 at 21:49 | history | edited | Andrés E. Caicedo | CC BY-SA 2.5 |
edited title
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| Oct 16, 2010 at 20:46 | comment | added | darij grinberg | I remember seeing the original poster's observation as an exercise on an IMO shortlist or in a similar source. Any idea where it was? (Not that it would really matter.) | |
| Oct 16, 2010 at 19:18 | comment | added | Richard Borcherds | These observations are part of the calculus of finite differences: see en.wikipedia.org/wiki/Calculus_of_finite_difference for more information | |
| Oct 16, 2010 at 19:03 | comment | added | dvitek | You write, "Many (all?) integer sequences $f(k)$ where $k = 1, 2, \cdots, n$ can be generated by a polynomial of degree $k-1$." I believe you mean $n-1$, and an explicit form for this polynomial is given by the Lagrange interpolation theorem. (The Wikipedia article on Lagrange polynomials has more details.) | |
| Oct 16, 2010 at 18:58 | answer | added | Alfonso Gracia-Saz | timeline score: 7 | |
| Oct 16, 2010 at 18:56 | answer | added | Qiaochu Yuan | timeline score: 15 | |
| Oct 16, 2010 at 18:21 | history | asked | Bob Andriesse | CC BY-SA 2.5 |