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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.

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  • 4
    $\begingroup$ 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. $\endgroup$ – Lynn Apr 15 '15 at 21:22
  • $\begingroup$ Number sequences puzzles are awful when no hint is given! $\endgroup$ – leoll2 Apr 16 '15 at 16:08
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Sequence 3 is:

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

n    n^0.5       nth digit
1 1.00 1
2 1.414 4
3 1.7321 3
4 2.00000 0
5 2.236068 0
6 2.4494897 8
7 2.64575131 1
8 2.828427125 1
9 3.0000000000 0
10 3.16227766017 0
11 3.316624790355 3

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  • $\begingroup$ Nice. How did you do that? $\endgroup$ – FLash Nov 6 '18 at 10:42
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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

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