1. ## fun series

Complete the last term of the series:

1)1, 6, 1, 8, 0, 3, 3, 9, 8,...
2)31, 41, 59, 26, 53, 58,...
3)0, 6, 21, 81, 42, 03,...
4)1, 8, 11, 80, 81,...
5)0, 1, 1, 2, 1, 3, 1, 3, 2, 3, 1,...
6)1476, 168, 48, 32, 6,...
7)1, 2, 3, 6, 9, 54, 63, 3402,...
8)291, 482, 864, 628, 246,...
9)1, 2, 2, 4, 2, 4, 2, 4, 6,...
10)1, 1, 2, 4, 8, 16, 23, 28, 38, 49,...
11)2, 2, 4, 4, 2, 6, 6, 2, 8, 8,...
12)0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3,...
13)1/1, 2/3, 3/4, 4/7, 5/6, 6/12, 7/8,...
14)141, 421, 356, 237, 309,...
15)0, 1, 8, 11, 69, 88, 96, 101,...
16)31, 28, 31, 30, 31, 30, 31,...
17)0, 1, 4, 6, 8, 9, 10, 12,...

2. The On-Line Encyclopedia of Integer Sequences

put every sequence there...

3. I'm sorry, I didn't knew of the existence of that site. However, there are some series that aren't there:

1)0, 6, 21, 81, 42, 03,...
2)1, 8, 11, 80, 81,...
3)1476, 168, 48, 32, 6,...
4)291, 482, 864, 628, 246,...
5)141, 421, 356, 237, 309,...

Send me an e-mail to pepearg2009@hotmail.es
And I may give you some answers (in exchange of anothers, we both know what we are talking about)

5. 1) Write the sequence backwards and group into pairs (except the last two) you end up with
30,24,18,12,6,0. So the number which completes the original sequence is 36
2) Increasing sequence of numbers beginning with vowels
3) Products of digits.
4) Double. If the result is less than 1000, take away 100, if it is greater than 1000, take away 1100.
5) Decimal expansion of root 2

6. Hello, brainteaser!

1) 1, 6, 1, 8, 0, 3, 3, 9, 8, ...
Digits of $\phi$, the Golden Mean.
. . Next number: .9

15) 0, 1, 8, 11, 69, 88, 96, 101, ...
Numbers that remain the same when rotated 180°.
. . Next number: .111

[The last invertible year was 1961 . . . The next is 6009.]