# Solve the numeric sequence

I've thrown together some fun sequences to stretch your brains out! You can feel free to provide as many additional members of the sequence as you'd like, but mostly I'm looking to see if you can solve the sequence. Here are the first three, which are all around the same difficulty:

1) 1, 5, 6, 2, 5, 4, 24, 9, 3,...
2) 73, 146, 219, 159, 86, 159, 232, 305, 161,...
3) 1, 4, 3, 0, 0, 8, 1, 1, 0,...

The final one here is a bit of a, shall we say, curveball:

4) 22, 34, 35, 22, 5, 6, 33, 84, 34,...

Have fun, and good luck!

EDIT 1: I thought I'd give a day or so to see if anyone could grasp the first three - I see one of them has been discovered already. :) I'll add hints for the other two:

Hint for 2)

Pay close attention to multiples and simple addition here.

Hint for 3)

It's no coincidence at all that each number is only one digit.

• Maybe add some hints for 1, 2, and 3? Number sequences are not very much to work with; 1 and 3 in particular barely seem arithmetic in nature anyway. We can't read your mind.
– Lynn
Apr 15, 2015 at 21:22
• Number sequences puzzles are awful when no hint is given! Apr 16, 2015 at 16:08

Sequence 3 is:

the $n^{th}$ digit of the square root of $n$, as follows:

n    n^0.5       nth digit1  1.00            12  1.414           43  1.7321          34  2.00000         05  2.236068        06  2.4494897       87  2.64575131      18  2.828427125     19  3.0000000000    010 3.16227766017   011 3.316624790355  3

• Nice. How did you do that? Nov 6, 2018 at 10:42

A quick search on http://oeis.org/ returned the first sequence. Even with the match, it took me some time to understand it :)

For the first sequence:

it is the square root of the smallest square composed with the rank numbers with zero of more additional numbers
n = 1 | smallest compound square = 1 | square root = 1
n = 2 | smallest compound square = 25 | square root = 5
n = 3 | smallest compound square = 36 | square root = 6
n = 4 | smallest compound square = 4 | square root = 2
n = 5 | smallest compound square = 25 | square root = 5
n = 6 | smallest compound square = 16 | square root = 4
n = 7 | smallest compound square = 576 | square root = 24
n = 8 | smallest compound square = 81 | square root = 9
n = 9 | smallest compound square = 9 | square root = 3
and so on...

Still working on the 3 others