Easy! 1, 1, 2, 3, 5, 8, 13, 21, 34, ? Give up?
Pretty easy! 1, 1, 1, 3, 5, 9, 17, 31, 57, ? Give up?
Easy! Fish in a big pond, perhaps? 1, 3, 7, 15, 31, 63, 127, 255, ? Give up?
Still really easy! 1, 8, 11, 69, 88, 96, 101, 111, 181, 609, ? Give up?
Classic, easy, supremely important: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, ? Give up?
You knew they were not all going to be easy! 1, 2, 4, 6, 10, 12, 16, 18, 22, ? Give up?
Those number sequences are all in the Online Encyclopedia of Integer Sequences (or OEIS).
But the real purpose of the OEIS is not puzzles, but identifying and
studying number sequences that have come up in people's work.
Here is a sequence that we are currently working on:
4
56
340
1120
3264
(Definition)
You won't be able to guess a formula, because no one in the world knows one!
Click the numbers to see gorgeous pictures of what we are counting (the number of regions).
To learn more about the sequences in the OEIS, watch the popular (4 million views!)
videos that Brady Haran and Neil Sloane have put on Youtube/Numberphile:
What Number Comes Next?; Terrific Toothpick Patterns; The Trapped Knight; How many ways can circles overlap?; Peaceable Queens; Don't Know (the Van Eck Sequence); Amazing Graphs (I); Amazing Graphs (II); Amazing Graphs (III); Primes on the Moon (Lunar Arithmetic). There is also a Numberphile Podcast, The Number Collector.
The OEIS gets millions of hits a week, and is often called one of the most useful mathematics sites on the Web. Over 8000 articles have referenced it, often saying "we discovered this result with the help of the OEIS". The database was started by Neil Sloane in 1964, and 56 years and 300,000 sequences later, he still runs it. These days he is a visiting professor in the Mathematrics Dept. at Rutgers University in Piscataway, NJ.
