Search Results
| Search type | Search syntax |
|---|---|
| Tags | [tag] |
| Exact | "words here" |
| Author |
user:1234 user:me (yours) |
| Score |
score:3 (3+) score:0 (none) |
| Answers |
answers:3 (3+) answers:0 (none) isaccepted:yes hasaccepted:no inquestion:1234 |
| Views | views:250 |
| Code | code:"if (foo != bar)" |
| Sections |
title:apples body:"apples oranges" |
| URL | url:"*.example.com" |
| Saves | in:saves |
| Status |
closed:yes duplicate:no migrated:no wiki:no |
| Types |
is:question is:answer |
| Exclude |
-[tag] -apples |
| For more details on advanced search visit our help page | |
Results tagged with integer-sequences
Search options answers only
not deleted
user 297
For questions about sequences of integers. References are often made to the online resource oeis.org.
10
votes
A possible surprise involving Euler's constant $e$
Sure.
$$c_n = \frac{1}{n+1} + \frac{1}{(n+1)(n+2)}+ \frac{1}{(n+1)(n+2)(n+3)} \cdots$$
so
$$\frac{1}{n+1} < c_n < \frac{1}{n+1}+\frac{1}{(n+1)^2}+\frac{1}{(n+1)^3}+\cdots = \frac{1}{n}.$$
That prov …
- 156k
4
votes
Accepted
On one class of Somos-like sequences
I believe this is a special case of Case (9) in Theorem 3.9 of Allman, Cuenca and Huang. By the way, this paper was an REU project!
- 156k
21
votes
Is the sequence $a_n=c a_{n-1} - a_{n-2}$ always composite for $n > 5$?
Put $u = (c + \sqrt{c^2-4})/2$. We have
$$a_{2n} = \frac{u^{2n}-u^{-2n}}{u-u^{-1}} = \left( \frac{ u^n-u^{-n}}{u-u^{-1}} \right) \left( \vphantom{\frac{ u^n-u^{-n}}{u-u^{-1}}} u^n + u^{-n} \right)$$
…
- 156k